Research Seminar: Cohomology of modular curves and local Langlands for GL2  

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 29Overview and motivationUlrich Görtz
May 6Admissible representationsJohan Bosman
May 20Galois representationsYamidt Bermudez Tobon
May 27The local Langlands correspondencePhilipp Hartwig
June 10Geometry of modular curves IMartin Kreidl
June 17Geometry of modular curves IIJuan Marcos Cerviño
June 24Eichler-Shimura theoryNicolas Billerey
July 1Decomposition of the representation sigma_pTONG Jilong
July 8Analysis of sigma_1PARK Donghoon
July 15Deformations of formal groups and the fundamental local representation IChristian Kappen
July 22Deformations of formal groups and the fundamental local representation II