Bloch-Beilinson conjectures for Hecke characters and Eisenstein cohomologyof Picard surfaces

Zoom ID: 919 6497 4060
For password contact Pieter Moree (moree@mpim-bonn.mpg.de)

Consider an algebraic Hecke character f of a number field and the associated pure Hodge structure H_f, which we will suppose of odd weight.
If the sign of the functional equation of the L-function L(f,s) is -1, thenL(f,s) vanishes at the central point. As a consequence, the Bloch-Beilinson conjectures predict in particular the existence of a non-trivial extension, of geometric origin, of the trivial Hodge structure by a twist of H_f, in the category of mixed Hodge structures. In this talk, I will report on joint work in progress with J. Bajpai, in which we construct the desired extension for a certain family of Hecke characters of an imaginary quadratic field, satisfying both the sign hypothesis above and the additional requirement that the order of vanishing of L(f,s) at the central point is equal to 1. The extension is constructed by means of the geometry of Picard surfaces and by employing crucially some results on their Eisenstein cohomology proven by G. Harder.