A New Approach to the Local Langlands Correspondence for GL_n Over p-Adic Fields

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:A New Approach to the Local Langlands Correspondence for GL_n Over p-Adic Fields
Speaker:Peter Scholze
Affiliation:University of Bonn
Date:Wednesday, November 17
Time/Room:2:15pm - 3:15pm/S-101

We give a new local characterization of the Local Langlands Correspondence, using deformation spaces of p-divisible groups, and show its existence by a comparison with the cohomology of some Shimura varieties. This reproves results of Harris-Taylor on the compatibility of local and global correspondences, but completely avoids the use of Igusa varieties and instead relies on the classical method of counting points a la Langlands and Kottwitz. Further, we have a new proof of bijectivity of this correspondence, relying on a description of the inertia-invariant nearby cycles in certain situations.