BIMSA-YMSC Tsinghua Number Theory Seminar | Kolyvagin's conjecture and Iwasawa theory

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.

Speaker

I am Chargée de Recherche with the CNRS at LAGA since October 2022. I visited the MSRI for the special programme Algebraic Cycles, L-Values, and Euler Systems from January till May 2023. Previosuly, I was an FSMP postdoc at LAGA with Jacques Tilouine and before that, I was a Ph.D. student at the London School of Geometry and Number Theory working under the supervision of Sarah Zerbes.