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1 results

  • Limites dégénérées de séries discrètes, formes automorphes et variétés de Griffiths–Schmid: le cas du groupe U (2, 1)

  • HENRI CARAYOL
  • Journal:
    Compositio Mathematica / Volume 111 / Issue 1 / March 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 51-88
    Print publication:
    March 1998
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  • Let $G$ be an inner anisotropic form of an unitary group of 3 variables over Q, such that $G_R≃U(2,1)$, and π be an automorphic representation of G(A) whose archimedean component π∞ is a degenerate limit of discrete series; such a π never occurs in the cohomology (coherent or étale) of a Shimura variety. We show that however it does ‘appear’ in the coherent cohomology of some line bundle over an associated Griffiths-Schmid variety. Moreover we study cup products between such cohomology classes and some other automorphic cohomology classes and we prove some non-vanishing results.