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The Local Langlands correspondence for \GL_n over p-adic fields

Peter Scholze

Number 51
Author Prof. Dr. Peter Scholze
Project B01
Year 2010

We reprove the Local Langlands Correspondence for \GL_n over p-adic fields as well as the existence of \ell-adic Galois representations attached to (most) regular algebraic conjugate self-dual cuspidal automorphic representations, for which we prove a local-global compatibility statement as in the book of Harris-Taylor.
In contrast to the proofs of the Local Langlands Correspondence given by Henniart and Harris-Taylor our proof completely by-passes the numerical Local Langlands Correspondence of Henniart. Instead, we make use of a previous result describing the inertia-invariant nearby cycles in certain regular situations.

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