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arXiv · 2306.09696

The canonical dimension of modules for Iwasawa algebras

James Timmins
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Abstract

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 $GL_n(F)$, with central character, has finite length if its dual has canonical dimension two.

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James Timmins. 2023-06-16. The canonical dimension of modules for Iwasawa algebras. https://doi.org/10.1007/s00029-025-01108-8

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