#### Vol. 295, No. 1, 2018

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

### Julien Hauseux

Vol. 295 (2018), No. 1, 17–30
##### 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
Primary: 22E50