Scholarlink

<p>Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level <i>N</i> 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 <i>unique</i> newform of level <i>N</i> with reducible residual representation. When this criterion is satisfied, we deduce an <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="29_2024_1000_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(R={\mathbb {T}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo>=</mo> <mi mathvariant="double-struck">T</mi> </mrow> </math></EquationSource> </InlineEquation> theorem.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Explicit non-Gorenstein \(R={\mathbb {T}}\) via rank bounds I: deformation theory

  • 期刊论文

  • 发表日期：

    2025年1月21日

查看全文
  • Catherine Hsu,
  • Preston Wake,
  • Carl Wang-Erickson

摘要

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 \(R={\mathbb {T}}\) R = T theorem.