A New Approach to the Local Langlands Correspondence for GLnGLn Over p-Adic Fields - Peter Scholze скачать в хорошем качестве

A New Approach to the Local Langlands Correspondence for GLnGLn Over p-Adic Fields - Peter Scholze

A New Approach to the Local Langlands Correspondence for GLnGLn Over p-Adic Fields - Peter Scholze University of Bonn November 17, 2010 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. For more videos, visit http://video.ias.edu