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

Abstract

Let $G$ be a $p$-adic reductive group and $R$ be a noetherian Jacobson algebra over the ring ${\mathbb{Z}}_l$ of $l$-adic integers with $l\ne p$. 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 $R$.