Orateur(s)  Luis Garcia  Imperial College London,

Titre  Regularized theta lifts and currents on orthogonal Shimura varieties 
Date  09/02/2015 
Horaire  10:30 à 12:00 

Résume  $$ 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 Lfunction 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 Lfunction times certain a certain period on $\operatornameSp_4$.

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