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MSRI Evans Talk: Modulo p representations of GL(n,Q_p) September 22, 2014 (04:10 PM PDT - 05:00 PM PDT)
Parent Program: Geometric Representation Theory
Location: 60 Evans Hall, UC Berkeley
Speaker(s) Marie-France Vigneras (Université de Paris VII (Denis Diderot))
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An irreducible representation of GL(n,Q_p) modulo p (over an algebraically closed field C of characteristic p) has an invariant vector by 1 +pM(n,Z_p), but we do not know how to classify these representations (except for n = 2). This is false for complex representations. The aim of the lecture is to explain how or why results true when n = 2 (1994 Barthel-Livne, 2000 Breuil) successfully generalize or fail when n > 2 (2011 Herzig, Ollivier). The main motivation for studying the modulo p representations of GL(n,Q_p) comes from the general feeling that a Langlands correspondence with the modulo p representations of dimension n of the absolute Galois group of Qp exists, as it does for C of characteristic 0 (2000, Harris-Taylor, Henniart) or l p (2001).

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