# Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

 Equipe(s) : fa, tn, Responsables : Alexis Bouthier, Cong Xue Email des responsables : alexis.bouthier@imj-prg.fr, cong.xue@imj-prg.fr Salle : Adresse : Description

 Orateur(s) Sergey LYSENKO - Université Nancy1, Titre Périodes de Waldspurger géometriques Date 19/01/2006 Horaire 14:00 à 15:00 Diffusion Résume We will report on some results towards geometric Howe correspondence in the framework of the geometric Langlands program. Let Y be an etale two-sheeted covering of a smooth projective curve X. Consider the dual reductive pair G,H, where $G=GSp_{2n}$ and H is a form of $GO_{2m}$ over X that becomes trivial over Y. Write $Bun_G$ for the stack of G-torsors on X. We define the functors of theta-lifting between the derived categories on the stacks $Bun_H$ and $Bun_G$. For m=n=1 and H nonsplit we show that the theta-lifting from $D(Bun_H)$ to $D(Bun_G)$ commutes with Hecke functors with respect to the corresponding map of $L-groups L^H\to L^G$. This allows us to calculate the geometric Waldspurger periods of cuspidal automorphic sheaves on $Bun_2$ as well as Bessel periods of some sheaves on $GSp_4$ (for nonramified two-sheeted coverings of X). Salle Adresse