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

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(F) = p, we prove that the ordinary part functor OrdP 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.

local fields, reductive groups, admissible smooth representations, parabolic induction, ordinary parts, extensions
Mathematical Subject Classification 2010
Primary: 22E50
Received: 8 May 2017
Revised: 23 August 2017
Accepted: 7 December 2017
Published: 13 March 2018
Julien Hauseux
Département de Mathématiques
Université de Lille