Algebra & Number Theory

Parabolic induction and extensions

Julien Hauseux

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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.

Article information

Algebra Number Theory, Volume 12, Number 4 (2018), 779-831.

Received: 7 September 2016
Revised: 23 April 2017
Accepted: 25 May 2017
First available in Project Euclid: 28 July 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

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


Hauseux, Julien. Parabolic induction and extensions. Algebra Number Theory 12 (2018), no. 4, 779--831. doi:10.2140/ant.2018.12.779.

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