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

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. W...

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Veröffentlicht in:arXiv.org 2023-03
Hauptverfasser: Hsu, Catherine, Wake, Preston, Wang-Erickson, Carl
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2209.00556