The search for a p-adic local Langlands correspondence
Prof. Peter Schneider
University of Muenster, Germany.
30-11-07

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Abstract

Local Langlands correspondences are about relating representations of absolute Galois groups of local fields to representations of reductive linear groups over the same field. I will begin by reviewing the hierarchy of local Galois representations (discrete, l-adic, p-adic) as well as the classical local Langlands correspondence which deals with l-adic Galois representations. Then I will describe the very rough form a p-adic correspondence between on the one side p-adic Galois representations and on the other side p-adic Banach space representations of GL_n should have. Finally I will describe the basic ideas underlying recent work of Breuil and of Colmez in the case of 2-dimensional Galois representations over the field Q_p.