Yifeng Liu (Yale)

Beilinson-Bloch conjecture and arithmetic inner product formula

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.


Recording: https://us02web.zoom.us/rec/play/KmmSO_xl2qw3pJrAD5dX9pT6BtgIo-_2C9nD1mL...


The meeting will be open from 14.15 (local time) for a virtual coffee with the speaker. 

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