##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Yifeng Liu

#### Yale University

## 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.

Host: Claus Sorensen

### November 19, 2020

### 3:00 PM

### https://kskedlaya.org/nts.cgi

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