On the exactness of ordinary parts over a local field of characteristic $p$

Julien Hauseux

Published 2017-05-07Version 1

Let $G$ be a connected reductive group over a non-archimedean local field $F$ of characteristic $p$, $P$ be a parabolic subgroup of $G$, and $R$ be an artinian ring in which $p$ is nilpotent. We prove that the ordinary part functor $\mathrm{Ord}_P$ is exact on the category of admissible smooth $R$-representations of $G$. We derive some consequences about extensions between admissible smooth $R$-representations of $G$.