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

被引：0
|
作者：
Hsu, Catherine [1 ]
Wake, Preston [2 ]
Wang-Erickson, Carl [3 ]
机构：
[1] Swarthmore Coll, Dept Math & Stat, Swarthmore, PA 19081 USA
[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
来源：
SELECTA MATHEMATICA-NEW SERIES | 2025年 / 31卷 / 01期
关键词：
Galois representations; Modular forms; Non-optimal level; R = T theorem; MODULAR-REPRESENTATIONS;
D O I：
10.1007/s00029-024-01000-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Ribet has proven remarkable results about non-optimal levels of residually reducibleGalois representations. We focus on a non-optimal levelNthat is the product oftwo distinct primes and where the Galois deformation ring is not expected to beGorenstein. We prove a Galois-theoretic criterion for the deformation ring to be assmall as possible-that is, for there to be auniquenewform of level N with reducible residual representation. When this criterion is satisfied, we deduce an R = T theorem.
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页数：71
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