BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar Kolyvagin’s conjecture and Iwasawa theory
Kolyvagin’s conjecture and Iwasawa theory
Organizers
Hansheng Diao , Yueke Hu , Emmanuel Lecouturier , Cezar Lupu
Speaker
Giada Grossi
Time
Monday, April 22, 2024 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
Abstract
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 $E$.