This is the GitHub repository containing code related to the paper Galois groups of simple abelian varieties over finite fields and exceptional Tate classes by Santiago Arango-Piñeros, Sam Frengley, and Sameera Vemulapalli arXiv:2505.09589, DOI:10.48550/arXiv.2505.09589.

The code in this repository is written in Magma and tested on Magma V2.28-11.

Directory structure

• src contains the main intrinsics provided (in particular an implementation of Algorithm 6.2 and code to check in a weighted permutation representation is exceptional).

• scripts contains Magma scripts for verifying claims made in the article.

• 1-4-theorem-data contains a list of exceptional weighted permutation representations in dimensions 2, 3, 4, 5, and 6.

• Galois-Frob-Polys (the code associated to our previous joint article) is included as a submodule.