Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications

Details Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications

2005-11-21

arxiv.org/abs/math/0511531v2

Inventiones Math. 2009 vol 177 pp 239-280 and Compositio Math 2010 vol 146 part 2 pp. 367-403

Mathematics

Algebraic Geometry

83 pages, 13 figures, some minor changes

Scientific paper

In the geometric situation of the simple Shimura varieties of Kottwitz studied in Harris and Taylor's book, we describe the monodromy filtration of the vanishing cycles complex and the spectral sequence associated to it. We prove in particular that this filtration coincides with the weight one up to shift. Thanks to the Berkovich-Fargues' theorem, we deduce the description of the local monodromy filtration of the Deligne-Carayol model. In application, we obtain the description of the local components of cohomological automorphic representations of certains unitary groups, a global Jacquet-Langlands correspondence between two such groups and a proof of the weight-monodromy conjecture for the cohomology of these Shimura varieties.

Affiliated with

Also associated with

No associations

Rating

Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications 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 Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monodromy of the perverse sheaf of vanishing cycles of some simple Shimura varieties and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-384261