The aim of the seminar is to learn something about the local Langlands correspondence for GL(2) over Q_p, and in particular about the connection to the cohomology of modular curves. (This case has been known for a long time, based on the work of Langlands, Deligne and Carayol (among others). See Carayol's paper cited in the program.) We will not prove the local Langlands correspondence even in this case (for a proof, see the book by Bushnell and Henniart), but will learn about several methods and results which are useful for generalizations (such as the work of Harris and Taylor) and variants, and open perspectives, for instance to the p-adic Langlands program.

Program: pdf.

Organizers: G. Böckle, U. Görtz, G. Wiese

Dates: Thu, 10-12, T03 R04 D10. We start on April 29.



April 29 Overview and motivation Ulrich Görtz
May 6 Admissible representations Johan Bosman
May 20 Galois representations Yamidt Bermudez Tobon
May 27 The local Langlands correspondence Philipp Hartwig
June 10 Geometry of modular curves I Martin Kreidl
June 17 Geometry of modular curves II Martin Kreidl
June 24 Eichler-Shimura theory Nicolas Billerey
July 1 Decomposition of the representation sigma_p TONG Jilong
July 15 Analysis of sigma_1 Ulrich Görtz
July 22 Deformations of formal groups and the fundamental local representation Christian Kappen