Venue: MCM510
Title: Deligne's conjecture for Rankin-Selberg L-functions
Abstract: Deligne's conjecture generalizes the famous result by Euler that for a positive integer m, \zeta(2m) is a rational multiple of (2\pi i)^{2m}. The aim of this series of talks is to introduce a proof of Deligne's conjecture for Rankin-Selberg L-functions.
In talk 1, we shall see some basic examples and introduce Deligne's conjecture that relates motivic L-values with motivic periods.
In talk 2, we will formulate an automorphic variant of Deligne's conjecture for the Rankin-Selberg L-function over quadratic imaginary fields. This conjecture relates automorphic L-values with automorphic periods. We then explain a proof of this automorphic variant (ongoing joint work with H. Grobner, M. Harris and A.Raghuram).
In talk 3, we explain a conditional proof for relations between automorphic periods and motivic periods (joint work with H. Grobner and M. Harris), and finally deduce Deligne's conjecture for the tensor product of two automorphic motives. If time permits, we shall explain how to generalize the results from imaginary quadratic fields to CM fields.
