Title: Beilinson-Bloch conjecture and arithmetic inner product formula

Speaker: Prof. Yifeng Liu (Yale)

Time: 16:00-17:00, July 23, 2020 (Beijing Time)

Abstract: In this talk, we study the Chow group of the motive associated to a tempered global L-packet \pi of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification
 of \pi, if the central derivative L'(1/2,\pi) is nonvanishing, then the \pi-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow
 groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain \pi-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights
 in terms of the central derivative L'(1/2,\pi) and local doubling zeta integrals. This is a joint work with Chao Li.