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

Abstract

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.