中科院数学与系统科学研究院
数学研究所
学术报告
数论研讨班
报告人：邱聪灵 博士（MIT）
题 目：Symmetry of the modified diagonal
时 间：2023.12.04（星期一），09:00-09:45
地 点：数学院南楼N933/ 腾讯会议号：578-737-938 密码：1204
摘 要：The modified diagonal cycle on the triple product of a curve was first introduced by Gross and Schoen in the 90’s. This simply defined object holds fundamental importance in the study of the geometry and arithmetic of curves. One basic question is whether this cycle "deforms" to 0. Such deformation to 0 is implied by the non-vanishing of the central value of the triple product L-function, under the notorious Beilinson–Bloch conjecture (generalization of the Birch–Swinnerton-Dyer conjecture). One result in my work with W. Zhang confirms this implication for Shimura cuves. Our approach is representation theoretic. Other results will also be discussed.
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