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.