Explicit non-Gorenstein R=T via rank bounds II: Computational aspects

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.

50 pages. To appear in the proceedings of the Fifteenth Algorithmic Number Theory Symposium (ANTS-XV)

References in corpus (1)

• Explicit non-Gorenstein R=T via rank bounds II: Computational aspects

Cited by in corpus (2)

• Explicit non-Gorenstein R=T via rank bounds II: Computational aspects
• Explicit non-Gorenstein R=T via rank bounds I: Deformation theory