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- W3212811571 abstract "In this article, 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, which generalizes the Birch and Swinnerton-Dyer conjecture. 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 confirms the conjectural arithmetic inner product formula proposed by one of us, which generalizes the Gross--Zagier formula to higher dimensional motives." @default.
- W3212811571 created "2021-11-22" @default.
- W3212811571 creator A5003753200 @default.
- W3212811571 creator A5089847496 @default.
- W3212811571 date "2021-11-01" @default.
- W3212811571 modified "2023-10-06" @default.
- W3212811571 title "Chow groups and L-derivatives of automorphic motives for unitary groups" @default.
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- W3212811571 doi "https://doi.org/10.4007/annals.2021.194.3.6" @default.
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