Une étude des représentations modulo $p$ de SL(2,F)

Abstract

Following what Barthel-Livné and Breuil made for GL(2,F), we study mod $p$ representations of SL(2,F) for F a complete non-archimedean local field of residual characteristic p and with finite residue field. In particular, we link these representations to the mod p representations of GL(2,F) and, when F = Q_p, we give an explicit description of the so-called supersingular representations, that do appear by packets of size at most 2.

30 pages

Cited by in corpus (10)

• A classification of irreducible admissible mod p representations of p-adic reductive groups
• Parabolic induction and extensions
• Serre weight conjectures for $p$-adic unitary groups of rank 2
• Functorial properties of pro-$p$-Iwahori cohomology
• On the existence of admissible supersingular representations of $p$-adic reductive groups
• Geometrization of the Satake transform for mod $p$ Hecke algebras
• On Extensions of supersingular representations of ${\mathrm{SL}}_2({\mathbb{Q}}_p)$
• $p$-adic Banach space representations of $S{L}_2({\mathbb{Q}}_p)$
• From $p$-modular to $p$-adic Langlands correspondences for $U(1,1)({\mathbb{Q}}_{p^2}/{\mathbb{Q}}_p)$: deformations in the non-supercuspidal case
• Derived right adjoints of parabolic induction: an example