# 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.