Vol. 12, No. 4, 2018

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Parabolic induction and extensions

Julien Hauseux

Vol. 12 (2018), No. 4, 779–831

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.

$p$-adic reductive groups, mod p representations, parabolic induction, extensions, derived ordinary parts, Bruhat filtration
Mathematical Subject Classification 2010
Primary: 22E50
Received: 7 September 2016
Revised: 23 April 2017
Accepted: 25 May 2017
Published: 11 July 2018
Julien Hauseux
Département de Mathématiques
Université de Lille
Villeneuve d’Ascq