An automorphic version of the Deligne conjecture

The Deligne conjecture relates special values of a motivic
L-function and the Deligne period. When the motive is associated to the
tensor product of two automorphic representations, we may reformulate
this conjecture in terms of automorphic periods. In this talk, we will
present this reformulation and some known results for the reformed
conjecture over quadratic imaginary field. If time permits, we will
discuss the generalization to CM fields.