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A new approach to the Local Langlands Correspondence for $GL_n$ over $p$-adic fields

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Peter Scholze
U. Bonn
Wed, 04/08/2010 - 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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.

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