Morningside Center of Mathematics

Chinese Academy of Sciences

中国科学院晨兴数学中心

Morningside Center of Mathematics

Chinese Academy of Sciences

Title: | Beilinson-Bloch conjecture and arithmetic inner product formula |

Speaker: | Prof. Yifeng Liu (Yale) |

Time: | 2020-7-23, 16:00-17:00 |

Place: | http://www.mcm.ac.cn/activities/programs/znts/202006/t20200609_564205.html |

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. |

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