中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

 

报告人邱聪灵 博士 Yale University

 Vanishing of some algebraic cycles on powers of Shimura curves

  2022.12.13(星期),09:00-10:00

  点:腾讯会议:144-233-508密码:1729     

  要:For a smooth projective variety over a number field, the BeilinsonBloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data. In particular, it predicts the vanishing of some cycles under suitable cohomological conditions. We verify such vanishing on powers of Shimura curves,  for  CM 0-cycles and modified diagonal 1-cycles. Automorphy and  modularity play essential roles in the proofs.

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