Automorphic Lefschetz properties via $L^2$ cohomology

Mathieu Cossutta (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

In this paper one proves a special case of a conjecture by Nicolas Bergeron. This conjecture is a kind of automorphic Lefschetz property. It relates the primitive cohomology of a locally symmetric manifolds modeled on $U(p,q+r)$ to the primitive cohomology of some of its totally geodesic submanifolds that are locally symmetric and modeled on $U(p,q)$.

Mots clés: Lefschetz properties; shimura varieties; representation theory

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Mathieu Cossutta. Automorphic Lefschetz properties via $L^2$ cohomology. 2009. ⟨hal-00421219⟩