Sur une conjecture de Breuil-Herzig

Julien Hauseux

Published 2014-05-25, updated 2014-09-18Version 2

We prove a conjecture of Breuil and Herzig on the uniqueness of certain unitary continuous representations of a $p$-adic reductive group whose constituents are principal series. In order to do so, we partially compute Emerton's $\delta$-functor $\mathrm{H^\bullet Ord}_P$ of derived ordinary parts with respect to a parabolic subgroup on a principal series. We formulate a new conjecture on the extensions between admissible smooth mod $p$ representations of a $p$-adic reductive group and we prove it in the case of extensions by a principal series.