Explicit non-Gorenstein R=T via rank bounds II: Computational aspects
Number Theory
2023-03-17 v2
Abstract
This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for the deformation ring to be as small as possible. This paper focuses on the computations needed to verify this criterion. We adapt a technique developed by Sharifi to compute number fields with twisted-Heisenberg Galois group and prescribed ramification, and compute the splitting behavior of primes in these extensions.
Keywords
Cite
@article{arxiv.2209.00556,
title = {Explicit non-Gorenstein R=T via rank bounds II: Computational aspects},
author = {Catherine Hsu and Preston Wake and Carl Wang-Erickson},
journal= {arXiv preprint arXiv:2209.00556},
year = {2023}
}
Comments
50 pages. To appear in the proceedings of the Fifteenth Algorithmic Number Theory Symposium (ANTS-XV)