Title :

Parabolic induction and extensions

Author(s) :

Hauseux, Julien [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Algebra & Number Theory

Pages :

779-831

Publisher :

Mathematical Sciences Publishers

Publication date :

2018

ISSN :

1937-0652

HAL domain(s) :

Mathématiques [math]/Théorie des représentations [math.RT]
Mathématiques [math]/Théorie des nombres [math.NT]

English abstract : [en]

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 ...
Show more >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 $\delta$-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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL