Computing Selmer groups associated to mod p Galois representations
Number Theory
2025-12-23 v2
Abstract
We present methods to compute Selmer groups associated to mod p Galois representations rho over a number field K, with a particular focus on comparing their ranks with periods coming from cohomology classes associated to rho by Serre's conjecture. This provides evidence for a loose version of a "mod p Bloch-Kato conjecture", where the vanishing of a period is predicted to capture the presence of rank in a Selmer group. Our methods are explicit, and implemented in Magma.
Keywords
Cite
@article{arxiv.2512.12899,
title = {Computing Selmer groups associated to mod p Galois representations},
author = {Lewis Combes},
journal= {arXiv preprint arXiv:2512.12899},
year = {2025}
}