报告人：林明辉（华中师范大学）

邀请人：张庆

报告时间：2023年10月13日（星期五）10:40-12:10

报告地点：东三十二楼216室

报告题目：On the growth of Tate-Shafarevich groups in Zp-extension

报告摘要：Around the 1960s, Iwasawa established a regularity in the growth of the Sylow p-subgroup of the class groups of the intermediate subfields of a Zp-extension of a number field F. Later works of Mazur, Greenberg and Lee showed that the Tate-Shafarevich group of an elliptic curve E also possesses such a regular growth when the elliptic curve E in question has good ordinary reduction at p. When E has good supersingular reduction at p, it was only thanks to the vision of Kobayashi, and a subsequent follow-up work of Iovita and Pollack, that we have an asymptotic formula for the growth in Zp-extension at which the Mordell-Weil rank of E is bounded. In this talk, we will study the growth of the Tate-Shafarevich groups of an elliptic curve with good supersingular reduction at p over the anticyclotomic Zp-extension of an imaginary quadratic field under the generalized Heegner condition, where the latter condition forces the Mordell-Weil rank to be unbounded. This is a joint work with Antonio Lei and Katharina Mueller.