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

Julien Hauseux

Vol. 295 (2018), No. 1, 17–30

DOI: 10.2140/pjm.2018.295.17

Abstract

Let $G$ be a connected reductive group over a nonarchimedean local field $F$ of residue characteristic $p$, $P$ be a parabolic subgroup of $G$, and $R$ be a commutative ring. When $R$ is artinian, $p$ is nilpotent in $R$, and $char\left(F\right)=p$, we prove that the ordinary part functor ${Ord}_P$ is exact on the category of admissible smooth $R$-representations of $G$. We derive some results on Yoneda extensions between admissible smooth $R$-representations of $G$.

Keywords

local fields, reductive groups, admissible smooth representations, parabolic induction, ordinary parts, extensions

Mathematical Subject Classification 2010

Primary: 22E50

Milestones

Received: 8 May 2017

Revised: 23 August 2017

Accepted: 7 December 2017

Published: 13 March 2018