comparingreduciblereps
Science Score: 44.0%
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Low similarity (7.7%) to scientific vocabulary
Repository
Basic Info
- Host: GitHub
- Owner: IgnasiSanchez
- License: gpl-3.0
- Language: M
- Default Branch: main
- Size: 49.8 KB
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Metadata Files
README.md
Comparing Reducible Representations with mod p image a p-group
Authors: Freitas, Nuno; Sánchez-Rodríguez, Ignasi.
Our Paper: this will be in Arxiv soon
Prerequisites
You need to download Edgar Costa's polred for Magma https://github.com/edgarcosta/MagmaPolred
In Magma's v2.28-5 version the function SmallestGeneratingSet was introduced. If your Magma version is one from before, you won't have this function and the code might run slower, depending on how many generators Magma finds for your Galois groups.
How to run
After installing the prerequisites and cloning the project, you need to change the spec path for Edgar Costa's code in the file GreniesAlgorithm.m.
AttachSpec("PathToSpec");
You should also change the default parisize as it is recommeneded in Edgar Costa's repository.
The examples in the paper correspond to the procedures Example3Adic for the 3-adic example (section 7) and ExampleOfGrenie for the validation of our code using Grenié's example (section 6). They are both in GreniesAlgorithm.m. So, for example, running the example of Grenié would look like this:
load "GreniesAlgorithm.m";
middleExtensions := [];
ExampleOfGrenie(~middleExtensions);
This fills the list middleExtensions with the tower $K0 \subseteq K1\subseteq \dots K_S$ for this example.
To compute the minimal set of primes $T$ one can use FrobeniusWithRelativeDecGrp.m for the 3-adic example. Our code for the primes in Grenié's example is not uploaded yet, but it is the same as in the 3-adic example, using Magma's FrobeniusElement instead of computing the Decomposition Groups.
We thank John Voight and Stephan Elsenhans for the GaloisAutomorphismGroup.m file. This function uses the GaloisData from the GaloisGroup computations and recovers the automorphisms acting on the field. This function is much faster than using AutomorphismGroup in the Galois case.
Owner
- Login: IgnasiSanchez
- Kind: user
- Repositories: 4
- Profile: https://github.com/IgnasiSanchez
Citation (citation.bib)
@misc{git,
accessed = {2025-07-10},
author = {Sánchez-Rodríguez, Ignasi and Freitas, Nuno},
title = {{Comparing Galois Representations in the residually Reducible Case}},
howpublished = "\url{https://github.com/IgnasiSanchez/ComparingReducibleReps}",
}
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