Explicit non-Gorenstein \(R=\mathbb{T}\) via rank bounds. II: Computational aspects. (English) Zbl 1540.11057
Summary: 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.
For Part I see [The authors, “Explicit non-Gorenstein \(R=\mathbb{T}\) via rank bounds I: Deformation theory’, Preprint, arXiv:2209.00536].
For Part I see [The authors, “Explicit non-Gorenstein \(R=\mathbb{T}\) via rank bounds I: Deformation theory’, Preprint, arXiv:2209.00536].
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