Vendredi 27 Mai

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Vendredi 27 Mai
Heure: 10:30 - 12:00
Lieu: Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Résumé: Géométrie Arithmétique et Motivique - [annulé] Supercuspidal mod p representations of GL_2(F), beyond the generic unramified case -
Description: Michael ScheinLet F / Q_p be a p-adic field.  In contrast
to the situation for complex representations, no classification of the
irreducible supercuspidal mod p representations of GL_n(F) is known,
except in the case GL_2(Q_p).  If F / Q_p is unramified and r is a
generic irreducible two-dimensional mod p representation of the absolute
Galois group of F, then nearly 15 years ago Breuil and Paskunas gave a
beautiful construction of an infinite family of diagrams giving rise to
supercuspidal mod p representations of GL_2(F) with GL_2(O_F)-socle
determined by Serre’s modularity conjecture for r.  While their
construction is not exhaustive, various local-global compatibility
results obtained by a number of mathematicians in the intervening years
indicate that it is sufficiently general to capture the mod p local
Langlands correspondence for generic Galois representations.