Scholarlink

<p>Let <i>F</i> be a non-trivial finite extension of the <i>p</i>-adic numbers, and <i>G</i> be a compact <i>p</i>-adic Lie group whose Lie algebra is isomorphic to a split semisimple <i>F</i>-Lie algebra. We prove that the mod <i>p</i> Iwasawa algebra of <i>G</i> has no modules of canonical dimension one. One consequence is a new upper bound on the Krull dimension of the Iwasawa algebra. We also prove a canonical dimension-theoretic criterion for a mod <i>p</i> smooth admissible representation to be of finite length. Combining our results shows that any smooth admissible representation of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(GL_n(F)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <msub> <mi>L</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, with central character, has finite length if its dual has canonical dimension two.</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

The canonical dimension of modules for Iwasawa algebras

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月17日

查看全文
  • James Timmins

摘要

Let F be a non-trivial finite extension of the p-adic numbers, and G be a compact p-adic Lie group whose Lie algebra is isomorphic to a split semisimple F-Lie algebra. We prove that the mod p Iwasawa algebra of G has no modules of canonical dimension one. One consequence is a new upper bound on the Krull dimension of the Iwasawa algebra. We also prove a canonical dimension-theoretic criterion for a mod p smooth admissible representation to be of finite length. Combining our results shows that any smooth admissible representation of \(GL_n(F)\) G L n ( F ) , with central character, has finite length if its dual has canonical dimension two.