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 :

Orateur(s) Luis Garcia - Imperial College London,
Titre Regularized theta lifts and currents on orthogonal Shimura varieties
Horaire10:30 à 12:00
We will start by reviewing a conjecture of Beilinson relating the regulator of a higher Chow group of a variety $X$ defined over $\mathbb Q$ with the special value of an L-function attached to $X$. Then I will consider the case where $X$ is a Shimura variety attached to an orthogonal group $G$. I will briefly review the notion of a theta lift and will explain how to construct certain currents on $X$ related to regulator maps as regularised theta lifts for the dual pair $(\operatornameSp_4,G)$. We will show that in some cases these currents can be evaluated and that the result involves the special value of a certain automorphic L-function times certain a certain period on $\operatornameSp_4$.