Parabolic induction and extensions

Hauseux, Julien

doi:10.2140/ant.2018.12.779

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Parabolic induction and extensions

Julien Hauseux

Vol. 12 (2018), No. 4, 779–831

DOI: 10.2140/ant.2018.12.779

Abstract

Let $G$ be a $p$ -adic reductive group. We determine the extensions between admissible smooth mod $p$ representations of $G$ parabolically induced from supersingular representations of Levi subgroups of $G$ , in terms of extensions between representations of Levi subgroups of $G$ and parabolic induction. This proves for the most part a conjecture formulated by the author in a previous article and gives some strong evidence for the remaining part. In order to do so, we use the derived functors of the left and right adjoints of the parabolic induction functor, both related to Emerton’s $δ$ -functor of derived ordinary parts. We compute the latter on parabolically induced representations of $G$ by pushing to their limits the methods initiated and expanded by the author in previous articles.

Keywords

$p$-adic reductive groups, mod p representations, parabolic induction, extensions, derived ordinary parts, Bruhat filtration

Mathematical Subject Classification 2010

Primary: 22E50

Milestones

Received: 7 September 2016

Revised: 23 April 2017

Accepted: 25 May 2017

Published: 11 July 2018

Authors

Julien Hauseux
Département de Mathématiques Université de Lille Villeneuve d’Ascq France

Vol. 12, No. 4, 2018