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学术报告 - 代数几何和数论方向
Bloch--Kato conjecture for some Rankin-Selberg motives
肖梁 教授(北京大学国际数学中心)
2021年6月17日14:00-15:00  闵行数学楼402报告厅

*主持人:谢兵永 教授


The Birch and Swinnerton-Dyer conjecture is known in the case of rank 0 and 1 thanks to the foundational work of Kolyvagin and Gross-Zagier. In this talk, I will report on a joint work with Yifeng Liu, Yichao Tian, Wei Zhang, and Xinwen Zhu. We study the analogue and generalizations of Kolyvagin's result to the unitary Gan-Gross-Prasad paradigm. More precisely, our ultimate goal is to show that, under some technical conditions, if the central value of the Rankin-Selberg L-function of an automorphic representation of U(n)*U(n+1) is nonzero, then the associated Selmer group is trivial; Analogously, if the Selmer class of certain cycle for the U(n)*U(n+1)-Shimura variety is nontrivial, then the dimension of the corresponding Selmer group is one.