Year: 2025
Type: article
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 $$GL_n(F)$$ G L n ( F ) , with central character, has finite length if its dual has canonical dimension two.
Source: Selecta Mathematica
Author: James Timmins
Institution: University of Edinburgh
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4417423309