Extensions entre series principales p-adiques et modulo p de G(F)

Abstract

Let $G$ be a split connected reductive group over a finite extension $F$ of $Q_p$. We determine the extensions between unitary continuous $p$-adic and smooth mod $p$ principal series of $G(F)$ in the generic case. In order to do so, we compute Emerton's delta-functor ${{\mathrm{H}}^{\bullet }\mathrm{Ord}}_{B(F)}$ of derived ordinary parts with respect to a Borel subgroup on certain induced representations of $G(F)$ using a Bruhat filtration. These extensions come into play in the $p$-adic and mod $p$ Langlands programs.

55 pages, in French, minor changes

Cited by in corpus (7)

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• Sur une conjecture de Breuil-Herzig
• Automorphic L-invariants for reductive groups
• On the exactness of ordinary parts over a local field of characteristic $p$
• Conjectures and results on modular representations of ${\mathrm{GL}}_n(K)$ for a $p$-adic field $K$
• The Left Adjoint of Derived Parabolic Induction
• p-adic etale cohomology of period domains