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1 results

  • Conjecture de monodromie-poids pour quelques variétés de Shimura unitaires

  • Part of
  • Pascal Boyer
  • Journal:
    Compositio Mathematica / Volume 146 / Issue 2 / March 2010
    Published online by Cambridge University Press:
    26 January 2010, pp. 367-403
    Print publication:
    March 2010
    • Article
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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.