Automorphic motives for unitary groups and period relations

Lucio Guerberoff

Published 2015-12-12Version 1

In this paper we explore some properties of periods attached to automorphic representations of unitary groups over CM fields and the critical values of their $L$-functions. On the one hand, we express the critical values as Petersson norms of holomorphic automorphic forms. On the other hand, we express the Deligne period of a related motive to a product of quadratic periods. The relation between the two expressions, predicted by Deligne's conjecture, is shown to be true in most cases if one assumes Tate's conjecture. Our techniques are based on previous work by Harris treating the case of quadratic imaginary fields.