Mathematics – Number Theory
Scientific paper
2010-11-08
Mathematics
Number Theory
Scientific paper
For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible supercuspidal representations parametrized by a Z_l-algebra R, in a way compatible with extension of scalars. When R is a field of characteristic l, this gives a cohomological realization of the Langlands-Vigneras correspondence for supercuspidals, and a new proof of its existence. When R runs over complete local algebras, this provides bijections between deformations of matching mod-l representations. Roughly speaking, we can decompose "the supercuspidal part" of the l-integral cohomology as a direct sum, indexed by irreducible supercuspidals \pi mod l, of tensor products of universal deformations of \pi and of its two mates. Besides, we also get a virtual realization of both the semi-simple Langlands-Vigneras correspondence and the l-modular Langlands-Jacquet transfer for all representations, by using the cohomology complex and working in a suitable Grothendieck group.
Dat Jean-Francois
No associations
LandOfFree
Théorie de Lubin-Tate non abélienne l-entière 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 Théorie de Lubin-Tate non abélienne l-entière, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Théorie de Lubin-Tate non abélienne l-entière will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-491886