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

Abstract

Let $G$ be a connected reductive group over a non-archimedean 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 $\mathrm{char}(F)=p$, 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 results on Yoneda extensions between admissible smooth $R$-representations of $G$.

arXiv comment10 pages, reverted to v2

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Cited by in corpus (3)

• Functorial properties of generalised Steinberg representations
• p-adic etale cohomology of period domains
• Deformation rings and parabolic induction