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arXiv · 2209.00536

Explicit non-Gorenstein R=T via rank bounds I: Deformation theory

Catherine Hsu·Preston Wake·Carl Wang-Erickson
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Abstract

Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level $N$ that is the product of two distinct primes and where the Galois deformation ring is not expected to be Gorenstein. We prove a Galois-theoretic criterion for the deformation ring to be as small as possible -- that is, for there to be a unique newform of level $N$ with reducible residual representation. When this criterion is satisfied, we deduce an $R=\mathbb{T}$ theorem.

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Catherine Hsu, Preston Wake, Carl Wang-Erickson. 2022-09-01. Explicit non-Gorenstein R=T via rank bounds I: Deformation theory. https://doi.org/10.1007/s00029-024-01000-x

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