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Kolyvagin’s conjecture and Iwasawa theory

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

Giada Grossi

时间

2024年04月22日 10:00 至 11:00

地点

Shuangqing-B627

摘要

Let $E$ be a rational elliptic curve and $p$ be an odd prime of good ordinary reduction for $E$. In 1991 Kolyvagin conjectured that the system of cohomology classes derived from Heegner points on the $p$-adic Tate module of $E$ over an imaginary quadratic field $K$ is non-trivial. I will talk about joint work with A.Burungale, F.Castella, and C.Skinner, where we prove Kolyvagin's conjecture in the cases where an anticyclotomic Iwasawa Main Conjecture for $E/K$ is known. Moreover, our methods also yield a proof of a refinement of Kolyvagin's conjecture expressing the divisibility index of the Heegner point Kolyvagin system in terms of the Tamagawa numbers of $E$.