The canonical dimension of modules for Iwasawa algebras

• James Timmins ^[1]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-025-01108-8
• Enlaces
  • Texto completo
• Resumen

  • 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 G Ln(F), with central character, has finite length if its dual has canonical dimension two.

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