Explicit Non-Gorenstein ๐=๐ Via Rank Bounds I: Deformation Theory
Document Type
Article
Publication Date
2-2025
Published In
Selecta Mathematica
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 possibleโthat is, for there to be a unique newform of level N with reducible residual representation. When this criterion is satisfied, we deduce an ๐=๐ theorem.
Keywords
Galois representations, Modular forms, Non-optimal level, ๐=๐ theorum
Recommended Citation
Cathy Hsu, P. Wake, and C. Wang-Erickson.
(2025).
"Explicit Non-Gorenstein ๐=๐ Via Rank Bounds I: Deformation Theory".
Selecta Mathematica.
Volume 31,
Issue 1.
DOI: 10.1007/s00029-024-01000-x
https://works.swarthmore.edu/fac-math-stat/333
Comments
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