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arXiv · 2410.10881

A note on the admissibility of smooth simple $RG$-modules

Mihir Sheth
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Abstract

Let $G$ be a $p$-adic reductive group and $R$ be a noetherian Jacobson $\mathbb{Z}[1/p]$-algebra. In this note, we show that every smooth irreducible $R$-linear representation of $G$ is admissible using the finiteness result of Dat, Helm, Kurinczuk and Moss for Hecke algebras over $R$.

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Mihir Sheth. 2024-10-10. A note on the admissibility of smooth simple $RG$-modules. https://doi.org/10.4171/rsmup%2F148

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