Mathematics – Number Theory
Scientific paper
2004-12-18
Mathematics
Number Theory
31 pages; added conditional results in the case v|l
Scientific paper
We prove the compatibility of local and global Langlands correspondences for GL_n, which was proved up to semisimplification by Harris-Taylor. More precisely, for the n-dimensional l-adic representation R_l(\Pi) of the Galois group of a CM-field L attached to a conjugate self-dual regular algebraic cuspidal automorphic representation \Pi, which is square integrable at some finite place, we show that Frobenius semisimplification of the restriction of R_l(\Pi) to the decomposition group of a prime v of L not dividing l corresponds to \Pi_v by the local Langlands correspondence. As a corollary, we show the irreducibility of R_l(\Pi) when \Pi_v is square integrable for some finite place v outside l. We also obtain conditional results in the case v|l.
Taylor Richard
Yoshida Teruyoshi
No associations
LandOfFree
Compatibility of local and global Langlands correspondences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Compatibility of local and global Langlands correspondences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compatibility of local and global Langlands correspondences will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-332628