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

Julien Hauseux (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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 $G$.

Domaines: Théorie des représentations [math.RT]; Théorie des nombres [math.NT]

Julien Hauseux. On the exactness of ordinary parts over a local field of characteristic $p$. Pacific Journal of Mathematics, 2018, 295 (1), pp.17-30. ⟨10.2140/pjm.2018.295.17⟩. ⟨hal-03403871⟩