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Conjecture de monodromie-poids pour quelques variétés de Shimura unitaires

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry Algebraic number theory: global fields Algebraic groups

Published online by Cambridge University Press:  26 January 2010

Pascal Boyer
Pascal Boyer*
Affiliation:
Institut de mathématiques de Jussieu, Université Paris 6, 4 place Jussieu, 75005 Paris, France (email: boyer@math.jussieu.fr)
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Abstract

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In Boyer [Monodromy of perverse sheaves on vanishing cycles on some Shimura varieties, Invent. Math. 177 (2009), 239–280 (in French)], a sheaf version of the monodromy-weight conjecture for some unitary Shimura varieties was proved by giving explicitly the monodromy filtration of the complex of vanishing cycles in terms of local systems introduced in Harris and Taylor [The geometry and cohomology of some simple Shimura varieties (Princeton University Press, Princeton, NJ, 2001)]. The main result of this paper is the cohomological version of the monodromy-weight conjecture for these Shimura varieties, which we prove by means of an explicit description of the groups of cohomology in terms of automorphic representations and the local Langlands correspondence.

Keywords

variétés de Shimuramodules formelscorrespondances de Langlandscorrespondances de Jacquet–Langlandsfaisceaux perverscycles évanescentsfiltration de monodromieconjecture de monodromie-poids

MSC classification

Secondary: 14G22: Rigid analytic geometry 14G35: Modular and Shimura varieties 11R39: Langlands-Weil conjectures, nonabelian class field theory 14L05: Formal groups, $p$-divisible groups 11G45: Geometric class field theory
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 2 , March 2010 , pp. 367 - 403
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

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