@article {DHI,
    AUTHOR = {Dugger, Daniel and Hollander, Sharon and Isaksen, Daniel C.},
     TITLE = {Hypercovers and simplicial presheaves},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {136},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {9--51},
      ISSN = {0305-0041,1469-8064},
   MRCLASS = {18F20 (55U35)},
  MRNUMBER = {2034012},
MRREVIEWER = {Manuel\ Bullejos Lorenzo},
       DOI = {10.1017/S0305004103007175},
       URL = {https://doi.org/10.1017/S0305004103007175},
}

@article {EHIK-cd,
    AUTHOR = {Elmanto, Elden and Hoyois, Marc and Iwasa, Ryomei and Kelly,
              Shane},
     TITLE = {Cdh descent, cdarc descent, and {M}ilnor excision},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {379},
      YEAR = {2021},
    NUMBER = {3-4},
     PAGES = {1011--1045},
      ISSN = {0025-5831,1432-1807},
   MRCLASS = {14F42 (14A20)},
  MRNUMBER = {4238259},
MRREVIEWER = {Bj\o rn\ Ian\ Dundas},
       DOI = {10.1007/s00208-020-02083-5},
       URL = {https://doi.org/10.1007/s00208-020-02083-5},
}


@article {Voevodsky-cd,
    AUTHOR = {Voevodsky, Vladimir},
     TITLE = {Homotopy theory of simplicial sheaves in completely
              decomposable topologies},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {214},
      YEAR = {2010},
    NUMBER = {8},
     PAGES = {1384--1398},
      ISSN = {0022-4049,1873-1376},
   MRCLASS = {55U35 (14F05 18F20 18G30)},
  MRNUMBER = {2593670},
MRREVIEWER = {Kathryn\ P.\ Hess},
       DOI = {10.1016/j.jpaa.2009.11.004},
       URL = {https://doi.org/10.1016/j.jpaa.2009.11.004},
}


@article {CM,
    AUTHOR = {Clausen, Dustin and Mathew, Akhil},
     TITLE = {Hyperdescent and \'{e}tale {$K$}-theory},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {225},
      YEAR = {2021},
    NUMBER = {3},
     PAGES = {981--1076},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {18F25 (14F20 55N15)},
  MRNUMBER = {4296353},
MRREVIEWER = {Barry\ H.\ Dayton},
       DOI = {10.1007/s00222-021-01043-3},
       URL = {https://doi.org/10.1007/s00222-021-01043-3},
}


@book {HTT,
    AUTHOR = {Lurie, Jacob},
     TITLE = {Higher topos theory},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {170},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {2009},
     PAGES = {xviii+925},
      ISBN = {978-0-691-14049-0; 0-691-14049-9},
   MRCLASS = {18-02 (18B25 18E35 18G30 18G55 55U40)},
  MRNUMBER = {2522659},
MRREVIEWER = {Mark\ Hovey},
       DOI = {10.1515/9781400830558},
       URL = {https://doi.org/10.1515/9781400830558},
}

@article {LT-pb,
    AUTHOR = {Land, Markus and Tamme, Georg},
     TITLE = {On the {$K$}-theory of pullbacks},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {190},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {877--930},
      ISSN = {0003-486X,1939-8980},
   MRCLASS = {19D55 (19D50 19E08)},
  MRNUMBER = {4024564},
MRREVIEWER = {Guillermo\ Corti\~{n}as},
       DOI = {10.4007/annals.2019.190.3.4},
       URL = {https://doi.org/10.4007/annals.2019.190.3.4},
}

@article {Hoyois,
    AUTHOR = {Hoyois, Marc},
     TITLE = {A quadratic refinement of the
              {G}rothendieck-{L}efschetz-{V}erdier trace formula},
   JOURNAL = {Algebr. Geom. Topol.},
  FJOURNAL = {Algebraic \& Geometric Topology},
    VOLUME = {14},
      YEAR = {2014},
    NUMBER = {6},
     PAGES = {3603--3658},
      ISSN = {1472-2747,1472-2739},
   MRCLASS = {14F42 (11E81 55M20)},
  MRNUMBER = {3302973},
MRREVIEWER = {Daniel\ C.\ Isaksen},
       DOI = {10.2140/agt.2014.14.3603},
       URL = {https://doi.org/10.2140/agt.2014.14.3603},
}


@misc{Freudenthal,
      title={On $\mathbb{P}^1$-stabilization in unstable motivic homotopy theory}, 
      author={Aravind Asok and Tom Bachmann and Michael J. Hopkins},
      year={2023},
      eprint={2306.04631},
      archivePrefix={arXiv},
      primaryClass={math.AG}
}

@misc{Aravind,
	title = {Algebraic geometry from an {$\mathbb{A}^1$}-homotopic viewpoint},
	author={Asok, Aravind},
	year={2021}
}


@article {AHW1,
    AUTHOR = {Asok, Aravind and Hoyois, Marc and Wendt, Matthias},
     TITLE = {Affine representability results in {$\mathbb{A}^1$}-homotopy
              theory, {I}: vector bundles},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {166},
      YEAR = {2017},
    NUMBER = {10},
     PAGES = {1923--1953},
      ISSN = {0012-7094},
   MRCLASS = {14F42 (55R15)},
  MRNUMBER = {3679884},
MRREVIEWER = {Kyle M. Ormsby},
       DOI = {10.1215/00127094-0000014X},
       URL = {https://doi-org.proxy.library.upenn.edu/10.1215/00127094-0000014X},
}


@article {AHW2,
    AUTHOR = {Asok, Aravind and Hoyois, Marc and Wendt, Matthias},
     TITLE = {Affine representability results in {$\mathbb{A}^1$}-homotopy
              theory, {II}: {P}rincipal bundles and homogeneous spaces},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {22},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {1181--1225},
      ISSN = {1465-3060},
   MRCLASS = {14F42 (14L10 20G15 55R15)},
  MRNUMBER = {3748687},
MRREVIEWER = {Federico Binda},
       DOI = {10.2140/gt.2018.22.1181},
       URL = {https://doi-org.proxy.library.upenn.edu/10.2140/gt.2018.22.1181},
}


@article {AHW3,
    AUTHOR = {Asok, Aravind and Hoyois, Marc and Wendt, Matthias},
     TITLE = {Affine representability results in {$\mathbb{A}^1$}-homotopy
              theory {III}: finite fields and complements},
   JOURNAL = {Algebr. Geom.},
  FJOURNAL = {Algebraic Geometry},
    VOLUME = {7},
      YEAR = {2020},
    NUMBER = {5},
     PAGES = {634--644},
      ISSN = {2313-1691},
   MRCLASS = {14F42 (14L10 20G15 55R15)},
  MRNUMBER = {4156421},
MRREVIEWER = {Niall Taggart},
       DOI = {10.14231/ag-2020-023},
       URL = {https://doi-org.proxy.library.upenn.edu/10.14231/ag-2020-023},
}


 @inbook{Morel-ICM, address={Zuerich, Switzerland}, title={A1-algebraic topology}, ISBN={978-3-03719-022-7}, url={http://www.ems-ph.org/doi/10.4171/022-2/49}, DOI={10.4171/022-2/49}, abstractNote={We present some recent results in A1-algebraic topology, which means both in A1-homotopy theory of schemes and its relationship with algebraic geometry. This refers to the classical relationship between homotopy theory and (differential) topology. We explain several examples of “motivic” versions of classical results: the theory of the Brouwer degree, the classification of A1-coverings through the A1-fundamental group, the Hurewicz Theorem and the A1-homotopy of algebraic spheres, and the A1-homotopy classification of vector bundles. We also give some applications and perspectives.}, booktitle={Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006}, publisher={European Mathematical Society Publishing House}, author={Morel, Fabien}, editor={Sanz-Solé, Marta and Soria, Javier and Varona, Juan Luis and Verdera, Joan}, year={2007}, month=may, pages={1035–1059}, language={en} }


@misc{bachmannstrongly,
      title={Strongly {$\mathbb{A}^1$}-invariant sheaves (after F. Morel)}, 
      author={Tom Bachmann},
      year={2024},
      eprint={2406.11526},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2406.11526}, 
}

 @book{Morel, address={Berlin, Heidelberg}, series={Lecture Notes in Mathematics}, title={A1-Algebraic Topology over a Field}, volume={2052}, ISBN={978-3-642-29513-3}, url={http://link.springer.com/10.1007/978-3-642-29514-0}, DOI={10.1007/978-3-642-29514-0}, publisher={Springer Berlin Heidelberg}, author={Morel, Fabien}, year={2012}, collection={Lecture Notes in Mathematics}, language={en} }


@article {infinite-loop,
    AUTHOR = {Elmanto, Elden and Hoyois, Marc and Khan, Adeel A. and
              Sosnilo, Vladimir and Yakerson, Maria},
     TITLE = {Motivic infinite loop spaces},
   JOURNAL = {Camb. J. Math.},
  FJOURNAL = {Cambridge Journal of Mathematics},
    VOLUME = {9},
      YEAR = {2021},
    NUMBER = {2},
     PAGES = {431--549},
      ISSN = {2168-0930,2168-0949},
   MRCLASS = {14F42 (14C05 19E15 55P47)},
  MRNUMBER = {4325285},
MRREVIEWER = {Ferdinando\ Zanchetta},
       DOI = {10.4310/CJM.2021.v9.n2.a3},
       URL = {https://doi.org/10.4310/CJM.2021.v9.n2.a3},
}

 @book{HA, title={Higher Algebra}, author={Lurie, Jacob}, year={2017} }


@article{Choudhury-H,
   title={Connectivity of motivic H–spaces},
   volume={14},
   ISSN={1472-2747},
   url={http://dx.doi.org/10.2140/agt.2014.14.37},
   DOI={10.2140/agt.2014.14.37},
   number={1},
   journal={Algebraic & Geometric Topology},
   publisher={Mathematical Sciences Publishers},
   author={Choudhury, Utsav},
   year={2014},
   month=jan, pages={37–55} }


@book {Fulton,
    AUTHOR = {Fulton, William},
     TITLE = {Intersection theory},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A
              Series of Modern Surveys in Mathematics [Results in
              Mathematics and Related Areas. 3rd Series. A Series of Modern
              Surveys in Mathematics]},
    VOLUME = {2},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1998},
     PAGES = {xiv+470},
      ISBN = {3-540-62046-X; 0-387-98549-2},
   MRCLASS = {14C17 (14-02)},
  MRNUMBER = {1644323},
       DOI = {10.1007/978-1-4612-1700-8},
       URL = {https://doi.org/10.1007/978-1-4612-1700-8},
}

 @unpublished{Youcis, title={A brief discussion of torsors}, author={Youcis, Alex} }


@misc{Stacks,
    shorthand    = {Stacks},
    author       = {The {Stacks Project Authors}},
    title        = {\textit{Stacks Project}},
    howpublished = {\url{https://stacks.math.columbia.edu}},
    year         = {2018},
  }
  
@article {Dugger-univ,
    AUTHOR = {Dugger, Daniel},
     TITLE = {Universal homotopy theories},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {164},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {144--176},
      ISSN = {0001-8708,1090-2082},
   MRCLASS = {18G55 (18E20 55U10)},
  MRNUMBER = {1870515},
MRREVIEWER = {Manuel\ Bullejos Lorenzo},
       DOI = {10.1006/aima.2001.2014},
       URL = {https://doi.org/10.1006/aima.2001.2014},
}

@book {Friedlander,
    AUTHOR = {Friedlander, Eric M.},
     TITLE = {\'Etale homotopy of simplicial schemes},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {No. 104},
 PUBLISHER = {Princeton University Press, Princeton, NJ; University of Tokyo
              Press, Tokyo},
      YEAR = {1982},
     PAGES = {vii+190},
      ISBN = {0-691-08288-X},
   MRCLASS = {55P99 (14F35 55-02)},
  MRNUMBER = {676809},
MRREVIEWER = {V.\ P.\ Snaith},
}

@book {GoerssJardine,
    AUTHOR = {Goerss, Paul G. and Jardine, John F.},
     TITLE = {Simplicial homotopy theory},
    SERIES = {Progress in Mathematics},
    VOLUME = {174},
 PUBLISHER = {Birkh\"auser Verlag, Basel},
      YEAR = {1999},
     PAGES = {xvi+510},
      ISBN = {3-7643-6064-X},
   MRCLASS = {55U10 (18G55 55-01 55Pxx)},
  MRNUMBER = {1711612},
MRREVIEWER = {R.\ M.\ Vogt},
       DOI = {10.1007/978-3-0348-8707-6},
       URL = {https://doi.org/10.1007/978-3-0348-8707-6},
}

@book {Weibel,
    AUTHOR = {Weibel, Charles A.},
     TITLE = {An introduction to homological algebra},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {38},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1994},
     PAGES = {xiv+450},
      ISBN = {0-521-43500-5; 0-521-55987-1},
   MRCLASS = {18-01 (16-01 17-01 20-01 55Uxx)},
  MRNUMBER = {1269324},
MRREVIEWER = {Kenneth\ A.\ Brown},
       DOI = {10.1017/CBO9781139644136},
       URL = {https://doi.org/10.1017/CBO9781139644136},
}

@article {Hodge3,
    AUTHOR = {Deligne, Pierre},
     TITLE = {Th\'eorie de {H}odge. {III}},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
    NUMBER = {44},
      YEAR = {1974},
     PAGES = {5--77},
      ISSN = {0073-8301,1618-1913},
   MRCLASS = {14C30 (14F15)},
  MRNUMBER = {498552},
MRREVIEWER = {J.\ H. M. Steenbrink},
       URL = {http://www.numdam.org/item?id=PMIHES_1974__44__5_0},
}

@book {Hartshorne,
    AUTHOR = {Hartshorne, Robin},
     TITLE = {Algebraic geometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {No. 52},
 PUBLISHER = {Springer-Verlag, New York-Heidelberg},
      YEAR = {1977},
     PAGES = {xvi+496},
      ISBN = {0-387-90244-9},
   MRCLASS = {14-01},
  MRNUMBER = {463157},
MRREVIEWER = {Robert\ Speiser},
}

@misc{MilneLEC,
author={Milne, James S.},
title={Lectures on Etale Cohomology (v2.21)},
year={2013},
note={Available at www.jmilne.org/math/},
pages={202}
}

@misc{MilneAG,
author={Milne, James S.},
title={Algebraic Groups (v2.00)},
year={2015},
note={Available at www.jmilne.org/math/},
pages={528}
}

@article{Grothendieck-torsion,
  title={Torsion homologique et sections rationnelles},
  author={Grothendieck, Alexandre},
  journal={S{\'e}minaire Claude Chevalley},
  volume={3},
  pages={1--29},
  year={1958},
  language={fr}
}


@misc{chd,
	title = {Some remarks on {G}alois cohomology and linear algebraic groups},
	author={Halleck-{D}ub\'{e}, Connor},
	url={https://math.berkeley.edu/~chd/expo/Gal_Coh.pdf}	
}

@incollection {AE,
    AUTHOR = {Antieau, Benjamin and Elmanto, Elden},
     TITLE = {A primer for unstable motivic homotopy theory},
 BOOKTITLE = {Surveys on recent developments in algebraic geometry},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {95},
     PAGES = {305--370},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2017},
      ISBN = {978-1-4704-3557-8},
   MRCLASS = {14F42 (55R50)},
  MRNUMBER = {3727503},
MRREVIEWER = {Serge\ A.\ Yagunov},
       DOI = {10.1090/pspum/095/01637},
       URL = {https://doi.org/10.1090/pspum/095/01637},
}

@misc{Bachmann-K,
	title = {Algebraic $K$-theory from the viewpoint of motivic homotopy theory},
	author = {Bachmann, Tom},
	url = {https://www.mathematik.uni-muenchen.de/~bachmann/KGL-minicourse.pdf},
}


@article{Nisnevich-cd,
  title = {{{TIIE COMPLETELY DECOMPOSED TOPOLOGY ON SCHEMES AND ASSOCIATED DESCENT SPECTRAL SEQUENCES IN ALGEBRAIC K-THEORY}}},
  author = {Nisnevich, Yeo A},
  pages = {102},
  abstract = {Let X be a noetherian scheme of finite Krull dimension. A new Grothendieck topology on X. called the completely decomposed topology. is introduced, and the formalism of the corresponding cohomology and homotopy theories is developed. This formalism is applied to construct certain descent (or local-to-global) spectral sequences convergent to various algebraic K-groups of X, or to the homotopy groups of more general spectra. They refine the well-known Brown-Gersten spectral sequences.},
  langid = {english},
  file = {/Users/tbraz/Zotero/storage/K57P28IL/Nisnevich - TIIE COMPLETELY DECOMPOSED TOPOLOGY ON SCHEMES AND.pdf}
}


@book {Riehl,
    AUTHOR = {Riehl, Emily},
     TITLE = {Categorical homotopy theory},
    SERIES = {New Mathematical Monographs},
    VOLUME = {24},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2014},
     PAGES = {xviii+352},
      ISBN = {978-1-107-04845-4},
   MRCLASS = {18G55 (18D20 55U35)},
  MRNUMBER = {3221774},
MRREVIEWER = {David\ A.\ Blanc},
       DOI = {10.1017/CBO9781107261457},
       URL = {https://doi.org/10.1017/CBO9781107261457},
}

@article {Hollander,
    AUTHOR = {Hollander, Sharon},
     TITLE = {A homotopy theory for stacks},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {163},
      YEAR = {2008},
     PAGES = {93--124},
      ISSN = {0021-2172,1565-8511},
   MRCLASS = {18G55 (14A20 18D30 55U35)},
  MRNUMBER = {2391126},
MRREVIEWER = {Mark\ W.\ Johnson},
       DOI = {10.1007/s11856-008-0006-5},
       URL = {https://doi.org/10.1007/s11856-008-0006-5},
}

@misc{SAG,
	author={Lurie, Jacob},
	title={Spectral algebraic geometry},
	year={2018}
}

@article {Traverso,
    AUTHOR = {Traverso, Carlo},
     TITLE = {Seminormality and {P}icard group},
   JOURNAL = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3)},
  FJOURNAL = {Annali della Scuola Normale Superiore di Pisa. Classe di
              Scienze. Serie III},
    VOLUME = {24},
      YEAR = {1970},
     PAGES = {585--595},
      ISSN = {0391-173X},
   MRCLASS = {14.55 (16.00)},
  MRNUMBER = {277542},
MRREVIEWER = {P.\ Abellanas},
}

@article {MV,
    AUTHOR = {Morel, Fabien and Voevodsky, Vladimir},
     TITLE = {{${\bf A}^1$}-homotopy theory of schemes},
   JOURNAL = {Inst. Hautes \'{E}tudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'{E}tudes Scientifiques. Publications
              Math\'{e}matiques},
    NUMBER = {90},
      YEAR = {1999},
     PAGES = {45--143},
      ISSN = {0073-8301,1618-1913},
   MRCLASS = {14F35 (19E08)},
  MRNUMBER = {1813224},
MRREVIEWER = {Marc\ Levine},
       URL = {http://www.numdam.org/item?id=PMIHES_1999__90__45_0},
}

@article{AF-spheres,
   title={Algebraic vector bundles on spheres},
   volume={7},
   ISSN={1753-8416},
   url={http://dx.doi.org/10.1112/jtopol/jtt046},
   DOI={10.1112/jtopol/jtt046},
   number={3},
   journal={Journal of Topology},
   publisher={Wiley},
   author={Asok, Aravind and Fasel, Jean},
   year={2014},
   month=feb, pages={894–926}
}



@article {Hoyois6,
    AUTHOR = {Hoyois, Marc},
     TITLE = {The six operations in equivariant motivic homotopy theory},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {305},
      YEAR = {2017},
     PAGES = {197--279},
      ISSN = {0001-8708,1090-2082},
   MRCLASS = {14F42 (55P91)},
  MRNUMBER = {3570135},
MRREVIEWER = {Jeremiah\ Ben\ Heller},
       DOI = {10.1016/j.aim.2016.09.031},
       URL = {https://doi.org/10.1016/j.aim.2016.09.031},
}

@incollection {Weibel-KH,
    AUTHOR = {Weibel, Charles A.},
     TITLE = {Homotopy algebraic {$K$}-theory},
 BOOKTITLE = {Algebraic {$K$}-theory and algebraic number theory
              ({H}onolulu, {HI}, 1987)},
    SERIES = {Contemp. Math.},
    VOLUME = {83},
     PAGES = {461--488},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1989},
      ISBN = {0-8218-5090-3},
   MRCLASS = {18F25 (19D25)},
  MRNUMBER = {991991},
MRREVIEWER = {Barry\ H.\ Dayton},
       DOI = {10.1090/conm/083/991991},
       URL = {https://doi.org/10.1090/conm/083/991991},
}

@misc{AD-excision,
      title={$A^1$-homotopy groups, excision, and solvable quotients}, 
      author={Aravind Asok and Brent Doran},
      year={2009},
      eprint={0902.1564},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/0902.1564}, 
}

@misc{AO-contractible,
      title={$A^1$-homotopy theory and contractible varieties: a survey}, 
      author={Aravind Asok and Paul Arne Ostv{\ae}r},
      year={2019},
      eprint={1903.07851},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/1903.07851}, 
}

@article {HMH,
    AUTHOR = {Hoyois, Marc},
     TITLE = {From algebraic cobordism to motivic cohomology},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {702},
      YEAR = {2015},
     PAGES = {173--226},
      ISSN = {0075-4102,1435-5345},
   MRCLASS = {14F43 (14F42 55N22 55U35)},
  MRNUMBER = {3341470},
MRREVIEWER = {Christophe\ Cazanave},
       DOI = {10.1515/crelle-2013-0038},
       URL = {https://doi.org/10.1515/crelle-2013-0038},
}

@article{Shah,
   title={Parametrized higher category theory},
   volume={23},
   ISSN={1472-2747},
   url={http://dx.doi.org/10.2140/agt.2023.23.509},
   DOI={10.2140/agt.2023.23.509},
   number={2},
   journal={Algebraic Geometric Topology},
   publisher={Mathematical Sciences Publishers},
   author={Shah, Jay},
   year={2023},
   month=may, pages={509–644}
}


@phdthesis{Feld-thesis,
	title = {{M}ilnor-{W}itt sheaves and modules},
	author = {Feld, Niels},
	year = {2021}
}

@book {Kbook,
    AUTHOR = {Weibel, Charles A.},
     TITLE = {The {$K$}-book},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {145},
      NOTE = {An introduction to algebraic $K$-theory},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2013},
     PAGES = {xii+618},
      ISBN = {978-0-8218-9132-2},
   MRCLASS = {19-01},
  MRNUMBER = {3076731},
MRREVIEWER = {L.\ N.\ Vaserstein},
       DOI = {10.1090/gsm/145},
       URL = {https://doi.org/10.1090/gsm/145},
}

@book {Lam,
    AUTHOR = {Lam, T. Y.},
     TITLE = {Introduction to quadratic forms over fields},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {67},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2005},
     PAGES = {xxii+550},
      ISBN = {0-8218-1095-2},
   MRCLASS = {11Exx},
  MRNUMBER = {2104929},
MRREVIEWER = {K.\ Szymiczek},
       DOI = {10.1090/gsm/067},
       URL = {https://doi.org/10.1090/gsm/067},
}

@article {MilnorK,
    AUTHOR = {Milnor, John},
     TITLE = {Algebraic {$K$}-theory and quadratic forms},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {9},
      YEAR = {1969},
     PAGES = {318--344},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {18.20 (10.00)},
  MRNUMBER = {260844},
MRREVIEWER = {H.\ Bass},
       DOI = {10.1007/BF01425486},
       URL = {https://doi.org/10.1007/BF01425486},
}

@book {EKM,
    AUTHOR = {Elman, Richard and Karpenko, Nikita and Merkurjev, Alexander},
     TITLE = {The algebraic and geometric theory of quadratic forms},
    SERIES = {American Mathematical Society Colloquium Publications},
    VOLUME = {56},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2008},
     PAGES = {viii+435},
      ISBN = {978-0-8218-4329-1},
   MRCLASS = {11Exx (11-02 11E04 11E81 14C15 14C25)},
  MRNUMBER = {2427530},
MRREVIEWER = {Andrzej\ S\l adek},
       DOI = {10.1090/coll/056},
       URL = {https://doi.org/10.1090/coll/056},
}

@misc{Deglise,
      title={Notes on {M}ilnor-{W}itt {$K$}-theory}, 
      author={Fr\'{e}d\'{e}ric D\'{e}glise},
      year={2023},
      eprint={2305.18609},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2305.18609}, 
}

@misc{Carlier,
      title={Milnor-{W}itt {$K$}-theory and {W}itt {$K$}-theory of a field}, 
      author={Robin Carlier},
      year={2023},
      eprint={2306.16985},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2306.16985}, 
}

@article {Fasel-CW,
    AUTHOR = {Fasel, Jean},
     TITLE = {The {C}how-{W}itt ring},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {12},
      YEAR = {2007},
     PAGES = {275--312},
      ISSN = {1431-0635,1431-0643},
   MRCLASS = {14C15 (14C17 14F43)},
  MRNUMBER = {2350291},
MRREVIEWER = {Dan Edidin},
}

@article {AF-vb-spheres,
    AUTHOR = {Asok, Aravind and Fasel, Jean},
     TITLE = {Algebraic vector bundles on spheres},
   JOURNAL = {J. Topol.},
  FJOURNAL = {Journal of Topology},
    VOLUME = {7},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {894--926},
      ISSN = {1753-8416,1753-8424},
   MRCLASS = {14J60 (14F42 19D45 55S35)},
  MRNUMBER = {3252968},
MRREVIEWER = {Daniel\ C.\ Isaksen},
       DOI = {10.1112/jtopol/jtt046},
       URL = {https://doi.org/10.1112/jtopol/jtt046},
}

@article {Deglise-MH,
    AUTHOR = {D\'{e}glise, F.},
     TITLE = {Modules homotopiques},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {16},
      YEAR = {2011},
     PAGES = {411--455},
      ISSN = {1431-0635,1431-0643},
   MRCLASS = {14F42 (14C15 14C35)},
  MRNUMBER = {2823365},
MRREVIEWER = {Sung\ Myung},
}

@incollection {Deglise-finite-corr,
    AUTHOR = {D\'{e}glise, Fr\'{e}d\'{e}ric},
     TITLE = {Finite correspondences and transfers over a regular base},
 BOOKTITLE = {Algebraic cycles and motives. {V}ol. 1},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {343},
     PAGES = {138--205},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {2007},
      ISBN = {978-0-521-70174-7; 0-521-70174-0},
   MRCLASS = {14F42 (14C17 14C25)},
  MRNUMBER = {2385302},
MRREVIEWER = {Oliver\ R\"ondigs},
       DOI = {10.1017/CBO9780511721496.005},
       URL = {https://doi.org/10.1017/CBO9780511721496.005},
}

@article {Robalo,
    AUTHOR = {Robalo, Marco},
     TITLE = {{$K$}-theory and the bridge from motives to noncommutative
              motives},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {269},
      YEAR = {2015},
     PAGES = {399--550},
      ISSN = {0001-8708,1090-2082},
   MRCLASS = {14F42 (14A22 18D10 19E15)},
  MRNUMBER = {3281141},
MRREVIEWER = {Jens\ Hornbostel},
       DOI = {10.1016/j.aim.2014.10.011},
       URL = {https://doi.org/10.1016/j.aim.2014.10.011},
}

@Article{ArasonPfister,
author={Arason, J{\'o}n Kristinn
and Pfister, Albrecht},
title={Beweis des Krullschen Durchschnittsatzes f{\"u}r den Wittring},
journal={Inventiones mathematicae},
year={1971},
month={6},
day={01},
volume={12},
number={2},
pages={173-176},
issn={1432-1297},
doi={10.1007/BF01404657},
url={https://doi.org/10.1007/BF01404657}
}

@article {AF3,
    AUTHOR = {Asok, Aravind and Fasel, Jean},
     TITLE = {A cohomological classification of vector bundles on smooth
              affine threefolds},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {163},
      YEAR = {2014},
    NUMBER = {14},
     PAGES = {2561--2601},
      ISSN = {0012-7094,1547-7398},
   MRCLASS = {14J60 (14J30 19D45 55S35)},
  MRNUMBER = {3273577},
MRREVIEWER = {Mart\'i\ Lahoz},
       DOI = {10.1215/00127094-2819299},
       URL = {https://doi.org/10.1215/00127094-2819299},
}

@book {GS,
    AUTHOR = {Gille, Philippe and Szamuely, Tam\'as},
     TITLE = {Central simple algebras and {G}alois cohomology},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {165},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2017},
     PAGES = {xi+417},
      ISBN = {978-1-316-60988-0; 978-1-107-15637-1},
   MRCLASS = {16K20 (14C35 14F22 19C30)},
  MRNUMBER = {3727161},
}

@article{Cazanave,
  title = {Algebraic Homotopy Classes of Rational Functions},
  author = {Cazanave, Christophe},
  date = {2012},
  journaltitle = {Annales scientifiques de l'\'Ecole normale supérieure},
  shortjournal = {Ann. Sci. \'Ecole Norm. Sup.},
  volume = {45},
  number = {4},
  pages = {511--534},
  issn = {0012-9593, 1873-2151},
  doi = {10.24033/asens.2172},
  url = {http://smf4.emath.fr/Publications/AnnalesENS/4_45/html/ens_ann-sc_45_511-534.php},
  urldate = {2021-08-02},
  langid = {english},
}


@thesis{Cazanave-thesis,
  title = {Th\'{e}orie homotopique des sch\'{e}mas d'Atiyah et Hitchin},
  author = {Cazanave, Christophe},
  date = {2009},
  institution = {Universit\'{e} Paris 13},
  langid = {french},
}

@misc{ABH-nilpotent,
      title={On the Whitehead theorem for nilpotent motivic spaces}, 
      author={Aravind Asok and Tom Bachmann and Michael J. Hopkins},
      year={2024},
      eprint={2210.05933},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2210.05933}, 
}

@misc{BHQW,
      title={Making the motivic group structure on the endomorphisms of the projective line explicit}, 
      author={Viktor Balch Barth and William Hornslien and Gereon Quick and Glen Matthew Wilson},
      year={2023},
      eprint={2306.00628},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2306.00628}, 
}

@incollection {Trieste,
    AUTHOR = {Morel, Fabien},
     TITLE = {An introduction to {$\mathbb{A}^1$}-homotopy theory},
 BOOKTITLE = {Contemporary developments in algebraic {$K$}-theory},
    SERIES = {ICTP Lect. Notes},
    VOLUME = {XV},
     PAGES = {357--441},
 PUBLISHER = {Abdus Salam Int. Cent. Theoret. Phys., Trieste},
      YEAR = {2004},
      ISBN = {92-95003-21-7},
   MRCLASS = {19E08 (14F35 55-02)},
  MRNUMBER = {2175638},
MRREVIEWER = {Daniel\ C.\ Isaksen},
}

@misc{Hoyois-Steinberg,
	author = {Hoyois, Marc},
	title = {The {S}teinberg Relation},
	date = {2018},
	url = {https://hoyois.app.uni-regensburg.de/papers/steinberg.pdf},
}

@article {DI-Hopf,
    AUTHOR = {Dugger, Daniel and Isaksen, Daniel C.},
     TITLE = {Motivic {H}opf elements and relations},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {19},
      YEAR = {2013},
     PAGES = {823--871},
      ISSN = {1076-9803},
   MRCLASS = {14F42 (55Q45)},
  MRNUMBER = {3141814},
MRREVIEWER = {Kyle\ M.\ Ormsby},
       URL = {http://nyjm.albany.edu:8000/j/2013/19_823.html},
}

@article {Druzhinin,
    AUTHOR = {Druzhinin, Andrei},
     TITLE = {The naive {M}ilnor-{W}itt {K}-theory relations in the stable
              motivic homotopy groups over a base},
   JOURNAL = {Ann. K-Theory},
  FJOURNAL = {Annals of K-Theory},
    VOLUME = {6},
      YEAR = {2021},
    NUMBER = {4},
     PAGES = {651--671},
      ISSN = {2379-1683,2379-1691},
   MRCLASS = {14F42 (19E08 19E20)},
  MRNUMBER = {4382799},
MRREVIEWER = {Wataru\ Kai},
       DOI = {10.2140/akt.2021.6.651},
       URL = {https://doi.org/10.2140/akt.2021.6.651},
}

@article {GuillouIsaksen,
    AUTHOR = {Guillou, Bertrand J. and Isaksen, Daniel C.},
     TITLE = {The {$\eta$}-local motivic sphere},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {219},
      YEAR = {2015},
    NUMBER = {10},
     PAGES = {4728--4756},
      ISSN = {0022-4049,1873-1376},
   MRCLASS = {14F42 (55S10 55T15)},
  MRNUMBER = {3346515},
MRREVIEWER = {Paul\ G.\ Goerss},
       DOI = {10.1016/j.jpaa.2015.03.004},
       URL = {https://doi.org/10.1016/j.jpaa.2015.03.004},
}

@incollection {Morel-pi0,
    AUTHOR = {Morel, Fabien},
     TITLE = {On the motivic {$\pi_0$} of the sphere spectrum},
 BOOKTITLE = {Axiomatic, enriched and motivic homotopy theory},
    SERIES = {NATO Sci. Ser. II Math. Phys. Chem.},
    VOLUME = {131},
     PAGES = {219--260},
 PUBLISHER = {Kluwer Acad. Publ., Dordrecht},
      YEAR = {2004},
      ISBN = {1-4020-1834-7},
   MRCLASS = {19D45 (11E81 14F42 19G12 55P99)},
  MRNUMBER = {2061856},
MRREVIEWER = {Daniel\ C.\ Isaksen},
       DOI = {10.1007/978-94-007-0948-5\_7},
       URL = {https://doi.org/10.1007/978-94-007-0948-5_7},
}

@misc{Nikolaus-gp,
	author = {Nikolaus, Thomas},
	title = {The group completion theorem via localizations of ring spectra},
	date = {2017}
}

@article {McDuffSegal,
    AUTHOR = {McDuff, D. and Segal, G.},
     TITLE = {Homology fibrations and the group completion theorem},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {31},
      YEAR = {1976},
    NUMBER = {3},
     PAGES = {279--284},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {55D45},
  MRNUMBER = {402733},
MRREVIEWER = {Harold\ Hastings},
       DOI = {10.1007/BF01403148},
       URL = {https://doi.org/10.1007/BF01403148},
}

@article {PeterSanath,
    AUTHOR = {Devalapurkar, Sanath and Haine, Peter},
     TITLE = {On the {J}ames and {H}ilton-{M}ilnor splittings, and the
              metastable {EHP} sequence},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {26},
      YEAR = {2021},
     PAGES = {1423--1464},
      ISSN = {1431-0635,1431-0643},
   MRCLASS = {55P35 (14F42 18N60 55P40 55Q20)},
  MRNUMBER = {4334846},
MRREVIEWER = {Geoffrey\ M. L. Powell},
}

@incollection {TT,
    AUTHOR = {Thomason, R. W. and Trobaugh, Thomas},
     TITLE = {Higher algebraic {$K$}-theory of schemes and of derived
              categories},
 BOOKTITLE = {The {G}rothendieck {F}estschrift, {V}ol.\ {III}},
    SERIES = {Progr. Math.},
    VOLUME = {88},
     PAGES = {247--435},
 PUBLISHER = {Birkh\"auser Boston, Boston, MA},
      YEAR = {1990},
      ISBN = {0-8176-3487-8},
   MRCLASS = {19E08 (14C35 19D10)},
  MRNUMBER = {1106918},
MRREVIEWER = {Charles\ Weibel},
       DOI = {10.1007/978-0-8176-4576-2\_10},
       URL = {https://doi.org/10.1007/978-0-8176-4576-2_10},
}

@incollection {Quillen,
    AUTHOR = {Quillen, Daniel},
     TITLE = {Higher algebraic {$K$}-theory. {I}},
 BOOKTITLE = {Algebraic {$K$}-theory, {I}: {H}igher {$K$}-theories ({P}roc.
              {C}onf., {B}attelle {M}emorial {I}nst., {S}eattle, {W}ash.,
              1972)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {Vol. 341},
     PAGES = {85--147},
 PUBLISHER = {Springer, Berlin-New York},
      YEAR = {1973},
   MRCLASS = {18F25},
  MRNUMBER = {338129},
MRREVIEWER = {Stephen\ M.\ Gersten},
}

@article {MurthySwan,
    AUTHOR = {Murthy, M. Pavaman and Swan, Richard G.},
     TITLE = {Vector bundles over affine surfaces},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {36},
      YEAR = {1976},
     PAGES = {125--165},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {14F05},
  MRNUMBER = {439842},
MRREVIEWER = {G.\ Horrocks},
       DOI = {10.1007/BF01390007},
       URL = {https://doi.org/10.1007/BF01390007},
}

@article {KumarMurthy,
    AUTHOR = {Kumar, N. Mohan and Murthy, M. Pavaman},
     TITLE = {Algebraic cycles and vector bundles over affine three-folds},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {116},
      YEAR = {1982},
    NUMBER = {3},
     PAGES = {579--591},
      ISSN = {0003-486X},
   MRCLASS = {14F05 (14C15)},
  MRNUMBER = {678482},
MRREVIEWER = {G.\ Horrocks},
       DOI = {10.2307/2007024},
       URL = {https://doi.org/10.2307/2007024},
}

@article {Murthy94,
    AUTHOR = {Murthy, M. Pavaman},
     TITLE = {Zero cycles and projective modules},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {140},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {405--434},
      ISSN = {0003-486X,1939-8980},
   MRCLASS = {13C10 (13D15 14C17 14C25)},
  MRNUMBER = {1298718},
MRREVIEWER = {N.\ Mohan Kumar},
       DOI = {10.2307/2118605},
       URL = {https://doi.org/10.2307/2118605},
}

@article {Swan67,
    AUTHOR = {Swan, Richard G.},
     TITLE = {The number of generators of a module},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {102},
      YEAR = {1967},
     PAGES = {318--322},
      ISSN = {0025-5874,1432-1823},
   MRCLASS = {13.40 (18.00)},
  MRNUMBER = {218347},
MRREVIEWER = {Robert\ Gilmer},
       DOI = {10.1007/BF01110912},
       URL = {https://doi.org/10.1007/BF01110912},
}

@article{Serre-modulesprojectifs,
     author = {Serre, Jean-Pierre},
     title = {Modules projectifs et espaces fibr\'es \`a fibre vectorielle},
     journal = {S\'eminaire Dubreil. Alg\`ebre et th\'eorie des nombres},
     note = {talk:23},
     publisher = {Secr\'etariat math\'ematique},
     volume = {11},
     number = {2},
     year = {1958},
     zbl = {0132.41202},
     language = {fr},
     url = {http://www.numdam.org/item/SD_1957-1958__11_2_A9_0/}
}

@article {RSO,
    AUTHOR = {R\"{o}ndigs, Oliver and Spitzweck, Markus and Ostv{\ae}r, Paul
              Arne},
     TITLE = {The first stable homotopy groups of motivic spheres},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {189},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {1--74},
      ISSN = {0003-486X,1939-8980},
   MRCLASS = {14F42 (55Q45)},
  MRNUMBER = {3898173},
MRREVIEWER = {Markus\ Szymik},
       DOI = {10.4007/annals.2019.189.1.1},
       URL = {https://doi.org/10.4007/annals.2019.189.1.1},
}

@article {AF-splitting,
    AUTHOR = {Asok, Aravind and Fasel, Jean},
     TITLE = {Splitting vector bundles outside the stable range and
              {$\mathbb{A}^1$}-homotopy sheaves of punctured affine spaces},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {28},
      YEAR = {2015},
    NUMBER = {4},
     PAGES = {1031--1062},
      ISSN = {0894-0347,1088-6834},
   MRCLASS = {14F42 (13C10 14J60 19A13 19D45)},
  MRNUMBER = {3369908},
MRREVIEWER = {Daniel\ C.\ Isaksen},
       DOI = {10.1090/S0894-0347-2014-00818-3},
       URL = {https://doi.org/10.1090/S0894-0347-2014-00818-3}
}

@article{BGT,
  title={A universal characterization of higher algebraic {$K$}-theory},
  author={Blumberg, Andrew J and Gepner, David and Tabuada, Gon{\c{c}}alo},
  journal={Geometry \& Topology},
  volume={17},
  number={2},
  pages={733--838},
  year={2013},
  publisher={Mathematical Sciences Publishers}
}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Howard -- references for Betti Realization appendix

@article{GreenleesMay,
    title={Equivariant stable homotopy theory},
    author={Greenlees, John PC and May, J Peter},
    journal={Handbook of algebraic topology},
    volume={277},
    pages={323},
    year={1995},
    publisher={Citeseer}
}

@article{BehrensShah-C2betti,
    title={{$C_2$}-equivariant stable homotopy from real motivic stable homotopy},
    author={Behrens, Mark and Shah, Jay},
    journal={Annals of K-theory},
    volume={5},
    number={3},
    pages={411--464},
    year={2020},
    publisher={Mathematical Sciences Publishers}
}

@article{Bachmann-betti,
    title={Motivic and real {\'e}tale stable homotopy theory},
    author={Bachmann, Tom},
    journal={Compositio Mathematica},
    volume={154},
    number={5},
    pages={883--917},
    year={2018},
    publisher={London Mathematical Society}
}

@article {Hutchinson,
    AUTHOR = {Hutchinson, Kevin},
     TITLE = {A new approach to {M}atsumoto's theorem},
   JOURNAL = {$K$-Theory},
  FJOURNAL = {$K$-Theory. An Interdisciplinary Journal for the Development,
              Application, and Influence of $K$-Theory in the Mathematical
              Sciences},
    VOLUME = {4},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {181--200},
      ISSN = {0920-3036,1573-0514},
   MRCLASS = {19C20},
  MRNUMBER = {1081659},
MRREVIEWER = {L.\ N.\ Vaserstein and E.\ R.\ Wheland},
       DOI = {10.1007/BF00533156},
       URL = {https://doi.org/10.1007/BF00533156},
}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%Hamilton -- References for Unimodular Rows Appendix

@article{Fasel_2010,
  title={Some remarks on orbit sets of Unimodular Rows}, 
  volume={86}, 
  DOI={10.4171/cmh/216}, 
  number={1}, 
  journal={Commentarii Mathematici Helvetici}, 
  author={Fasel, Jean}, 
  year={2010}, 
  pages={13–39}
  } 

@article{LERBET2024109415,
title = {Motivic stable cohomotopy and unimodular rows},
journal = {Advances in Mathematics},
volume = {436},
pages = {109415},
year = {2024},
issn = {0001-8708},
doi = {https://doi.org/10.1016/j.aim.2023.109415},
url = {https://www.sciencedirect.com/science/article/pii/S0001870823005583},
author = {Samuel Lerbet},
keywords = {Motivic homotopy theory, Unimodular rows},
abstract = {We relate the group structure of van der Kallen on orbit sets of unimodular rows ([26]) with values in a smooth algebra A over a field k with the motivic cohomotopy groups of X=SpecA with coefficients in An∖0 in the sense of [5]. In the last section, we compare the motivic cohomotopy theory studied in this paper and defined by An+1∖0 or, equivalently, by an A1-weakly equivalent quadric Q2n+1 to that considered in [5], defined by a quadric Q2n, by means of explicit morphisms Q2n+1→Q2n, Q2n×Gm→Q2n+1 of quadrics.}
}

@article {AHW2,
    AUTHOR = {Asok, Aravind and Hoyois, Marc and Wendt, Matthias},
     TITLE = {Affine representability results in {$\mathbb{A}^1$}-homotopy
              theory, {II}: {P}rincipal bundles and homogeneous spaces},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {22},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {1181--1225},
      ISSN = {1465-3060},
   MRCLASS = {14F42 (14L10 20G15 55R15)},
  MRNUMBER = {3748687},
MRREVIEWER = {Federico Binda},
       DOI = {10.2140/gt.2018.22.1181},
       URL = {https://doi-org.proxy.library.upenn.edu/10.2140/gt.2018.22.1181},
}


@incollection {Lindel,
    AUTHOR = {Lindel, Hartmut},
     TITLE = {On projective modules over polynomial rings over regular
              rings},
 BOOKTITLE = {Algebraic {$K$}-theory, {P}art {I} ({O}berwolfach, 1980)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {966},
     PAGES = {169--179},
 PUBLISHER = {Springer, Berlin-New York},
      YEAR = {1982},
      ISBN = {3-540-11965-5},
   MRCLASS = {13C10 (13B25 13F20)},
  MRNUMBER = {689374},
MRREVIEWER = {Manuel\ Ojanguren},
}

@article {Vorst,
    AUTHOR = {Vorst, Ton},
     TITLE = {The general linear group of polynomial rings over regular
              rings},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {9},
      YEAR = {1981},
    NUMBER = {5},
     PAGES = {499--509},
      ISSN = {0092-7872,1532-4125},
   MRCLASS = {13B10 (13D15 13E99 20G35)},
  MRNUMBER = {606650},
MRREVIEWER = {Andy\ R.\ Magid},
       DOI = {10.1080/00927878108822596},
       URL = {https://doi.org/10.1080/00927878108822596},
}

@article{vdk,
title = {A module structure on certain orbit sets of unimodular rows},
journal = {Journal of Pure and Applied Algebra},
volume = {57},
number = {3},
pages = {281-316},
year = {1989},
issn = {0022-4049},
doi = {https://doi.org/10.1016/0022-4049(89)90035-2},
url = {https://www.sciencedirect.com/science/article/pii/0022404989900352},
author = {Wilberd van der {Kallen}},
abstract = {An algebraic version of cohomotopy groups is developed. Further the stabilization problem for the K1 of Bass is studied for matrices that are much smaller than those treated classically.},
shorthand = {Kal89}
}

@inproceedings{suslin2006mennicke,
  title={Mennicke symbols and their applications in the K-theory of fields},
  author={Suslin, Andrei A},
  booktitle={Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part I},
  pages={334--356},
  year={2006},
  organization={Springer}
}

@InProceedings{bass,
author="Bass, Hyman",
title="Lib{\'e}ration des modules projectifs sur certains anneaux de polyn{\^o}mes",
booktitle="S{\'e}minaire Bourbaki vol. 1973/74 Expos{\'e}s 436--452",
year="1975",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="228--254",
isbn="978-3-540-37310-0"
}



@incollection {vdk2,
    AUTHOR = {van der Kallen, Wilberd},
     TITLE = {From {M}ennicke symbols to {E}uler class groups},
 BOOKTITLE = {Algebra, arithmetic and geometry, {P}art {I}, {II} ({M}umbai,
              2000)},
    SERIES = {Tata Inst. Fund. Res. Stud. Math.},
    VOLUME = {16},
     PAGES = {341--354},
 PUBLISHER = {Tata Inst. Fund. Res., Bombay},
      YEAR = {2002},
      ISBN = {81-7319-476-9},
   MRCLASS = {19E20},
  MRNUMBER = {1940672},
MRREVIEWER = {L.\ N.\ Vaserstein},
}

@article {AF22,
    AUTHOR = {Asok, Aravind and Fasel, Jean},
     TITLE = {Euler class groups and motivic stable cohomotopy},
      NOTE = {With an appendix by Mrinal Kanti Das},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {24},
      YEAR = {2022},
    NUMBER = {8},
     PAGES = {2775--2822},
      ISSN = {1435-9855,1435-9863},
   MRCLASS = {14F42 (19E15 55Q55)},
  MRNUMBER = {4416590},
MRREVIEWER = {Matthias\ Wendt},
       DOI = {10.4171/jems/1156},
       URL = {https://doi.org/10.4171/jems/1156},
}

@article{SYED2024478,
title = {Symplectic orbits of unimodular rows},
journal = {Journal of Algebra},
volume = {646},
pages = {478-493},
year = {2024},
issn = {0021-8693},
doi = {https://doi.org/10.1016/j.jalgebra.2024.02.015},
url = {https://www.sciencedirect.com/science/article/pii/S0021869324000930},
author = {Tariq Syed},
keywords = {Symplectic group, Projective module, Stably free module, Vaserstein symbol, Cancellation},
abstract = {For a smooth affine algebra R of dimension d≥3 over a field k and an invertible alternating matrix χ of rank 2n, the group Sp(χ) of invertible matrices of rank 2n over R which are symplectic with respect to χ acts on the right on the set Um2n(R) of unimodular rows of length 2n over R. In this paper, we prove that Sp(χ) acts transitively on Um2n(R) if k is algebraically closed, d!∈k× and 2n≥d.}
}

@article {Bass_Schanuel,
    AUTHOR = {Bass, H. and Schanuel, S.},
     TITLE = {The homotopy theory of projective modules},
   JOURNAL = {Bull. Amer. Math. Soc.},
  FJOURNAL = {Bulletin of the American Mathematical Society},
    VOLUME = {68},
      YEAR = {1962},
     PAGES = {425--428},
      ISSN = {0002-9904},
   MRCLASS = {13.40 (18.20)},
  MRNUMBER = {152559},
MRREVIEWER = {F.\ Hirzebruch},
       DOI = {10.1090/S0002-9904-1962-10826-X},
       URL = {https://doi.org/10.1090/S0002-9904-1962-10826-X},
}

@article {quillen_serre_problem,
    AUTHOR = {Quillen, Daniel},
     TITLE = {Projective modules over polynomial rings},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {36},
      YEAR = {1976},
     PAGES = {167--171},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {13C10},
  MRNUMBER = {427303},
MRREVIEWER = {Daniel\ Lazard},
       DOI = {10.1007/BF01390008},
       URL = {https://doi.org/10.1007/BF01390008},
}



@article{Serre-modulesprojectifs,
     author = {Serre, Jean-Pierre},
     title = {Modules projectifs et espaces fibr\'es \`a fibre vectorielle},
     journal = {S\'eminaire Dubreil. Alg\`ebre et th\'eorie des nombres},
     note = {talk:23},
     publisher = {Secr\'etariat math\'ematique},
     volume = {11},
     number = {2},
     year = {1957-1958},
     zbl = {0132.41202},
     language = {fr},
     url = {http://www.numdam.org/item/SD_1957-1958__11_2_A9_0/}
}

@article {suslin_serre_conj,
    AUTHOR = {Suslin, A. A.},
     TITLE = {Projective modules over polynomial rings are free},
   JOURNAL = {Dokl. Akad. Nauk SSSR},
  FJOURNAL = {Doklady Akademii Nauk SSSR},
    VOLUME = {229},
      YEAR = {1976},
    NUMBER = {5},
     PAGES = {1063--1066},
      ISSN = {0002-3264},
   MRCLASS = {13C10 (13F20 14F05)},
  MRNUMBER = {469905},
MRREVIEWER = {H.\ Bass},
}

@book {Lam_Serre_Problem,
    AUTHOR = {Lam, T. Y.},
     TITLE = {Serre's problem on projective modules},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2006},
     PAGES = {xxii+401},
      ISBN = {978-3-540-23317-6; 3-540-23317-2},
   MRCLASS = {13C10},
  MRNUMBER = {2235330},
       DOI = {10.1007/978-3-540-34575-6},
       URL = {https://doi.org/10.1007/978-3-540-34575-6},
}

@article {borsuk,
    AUTHOR = {Borsuk, Karol},
     TITLE = {Remarks on the homotopic join of maps},
   JOURNAL = {Fund. Math.},
  FJOURNAL = {Polska Akademia Nauk. Fundamenta Mathematicae},
    VOLUME = {50},
      YEAR = {1962},
     PAGES = {195--206},
      ISSN = {0016-2736,1730-6329},
   MRCLASS = {55.40},
  MRNUMBER = {189025},
MRREVIEWER = {E.\ Duda},
       DOI = {10.4064/fm-50-2-195-206},
       URL = {https://doi.org/10.4064/fm-50-2-195-206},
}

@article{FAC,
  title = {Faisceaux Alg{\'e}briques Coh{\'e}rents},
  author = {Serre, Jean-Pierre},
  year = {1955},
  langid = {english},
  file = {/Users/tbraz/Zotero/storage/5G6S3IUR/Serre - Coherent Algebraic Sheaves.pdf;/Users/tbraz/Zotero/storage/XXF9AHA5/1955_Serre-FaisceauxAlgebriquesCoherents-FRENCH.pdf}
}

@misc{AF-survey,
      title={Vector bundles on algebraic varieties}, 
      author={Aravind Asok and Jean Fasel},
      year={2021},
      eprint={2111.03107},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      url={https://arxiv.org/abs/2111.03107}, 
}

@incollection{AF2,
  title = {Secondary Characteristic Classes and the {{Euler}} Class},
  booktitle = {A {{Collection}} of {{Manuscripts Written}} in {{Honour}} of {{Alexander S}}. {{Merkurjev}} on the {{Occasion}} of {{His Sixtieth Birthday}}},
  author = {Asok, Aravind and Fasel, Jean},
  editor = {Balmer, Paul and Chernousov, Vladimir and Garibaldi, Skip and Fesenko, Ivan and Friedlander, Eric M. and Rehmann, Ulf and Reichstein, Zinovy},
  year = {2015},
  month = jan,
  edition = {1},
  pages = {7--29},
  publisher = {EMS Press},
  doi = {10.4171/dms/7/2},
  urldate = {2023-07-18},
  abstract = {We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We then show that if X is a smooth affine scheme of dimension d over a field k of finite 2cohomological dimension (with char(k) = 2) and E is a rank d vector bundle over X, vanishing of the Chow-Witt theoretic Euler class of E is equivalent to vanishing of its top Chern class and these higher classes. We then derive some consequences of our main theorem when k is of small 2-cohomological dimension.},
  isbn = {978-3-936609-61-5 978-3-9854704-0-2},
  langid = {english},
  file = {/Users/tbraz/Zotero/storage/WTLVVAZY/Asok and Fasel - 2015 - Secondary characteristic classes and the Euler cla.pdf}
}

@book{SGA6,
  shorthand = {SGA6},
  title = {Th{\'e}orie Des {{Intersections}} et {{Th{\'e}or{\`e}me}} de {{Riemann-Roch}}},
  author = {Berthelot, P. and Grothendieck, A. and Illusie, L.},
  year = {1971},
  series = {Lecture {{Notes}} in {{Mathematics}}},
  number = {225},
  publisher = {Springer-Verlag},
  file = {/Users/tbraz/Zotero/storage/KS2V9Z4M/Berthelot et al. - 1971 - Th' e orie des Intersections et Th' e or` e me de Riemann-Roch.pdf}
}


@incollection{KS-Global,
  title = {Global Class Field Theory of Arithmetic Schemes},
  booktitle = {Contemporary {{Mathematics}}},
  author = {Kato, Kazuya and Saito, Shuji},
  editor = {Bloch, Spencer J. and Dennis, R. Keith and Friedlander, Eric M. and Stein, Michael R.},
  year = {1986},
  volume = {55.1},
  pages = {255--331},
  publisher = {American Mathematical Society},
  address = {Providence, Rhode Island},
  urldate = {2025-02-07},
  isbn = {978-0-8218-5055-8 978-0-8218-7641-1},
  langid = {english},
  file = {/Users/tbraz/Zotero/storage/XJCLKA7G/Kato and Saito - 1986 - Global class field theory of arithmetic schemes.pdf}
}


@article {Nis80,
    AUTHOR = {Nisnevich, E. A.},
     TITLE = {Arithmetic and cohomology invariants of semisimple group
              schemes and compactifications of locally symmetric spaces},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u i\ Analiz i ego
              Prilozheniya},
    VOLUME = {14},
      YEAR = {1980},
    NUMBER = {1},
     PAGES = {75--76},
      ISSN = {0374-1990},
   MRCLASS = {14L99 (14F20)},
  MRNUMBER = {565110},
MRREVIEWER = {Yu.\ G.\ Zarkhin},
}

@article{Tohoku,
  title = {Sur Quelques Points d'alg{\`e}bre Homologique},
  author = {Grothendieck, Alexander},
  year = {1957},
  journal = {The Tohoku Mathematical Journal. Second Series},
  volume = {9},
  pages = {119--221},
  issn = {0040-8735,2186-585X},
  doi = {10.2748/tmj/1178244839},
  mrnumber = {102537},
  file = {/Users/tbraz/Zotero/storage/R4UNY9TB/Grothendieck - 1957 - Sur quelques points d'algèbre homologique.pdf;/Users/tbraz/Zotero/storage/UMPS5ZSJ/Tohoku-English.pdf}
}