Seminario Teoría de Números

Title: ON KOLYVAGIN'S CONJECTURE AND THE BLOCH-KATO FORMULA FOR MODULAR FORMS


SPEAKER: Stefano Vigno (Università degli Studi Genova)

DATE & TIME: Tuesday, 18th June 2019 - 11:30

VENUE: Aula 420, Módulo 17, Dpto. de Matemáticas, UAM

ORGANISER: UAM - ICMAT

ABSTRACT: A few years ago, Wei Zhang proved (under certain assumptions) Kolyvagin's conjecture on the non-triviality of his system of cohomology classes built out of the Euler system of Heegner points on a rational elliptic curve. He also proved the p-part of the Birch and Swinnerton-Dyer formula in analytic rank one. In this talk I will describe an analogue of Kolyvagin's conjecture for Heegner cycles on Kuga-Sato varieties and state the p-part of the Bloch-Kato formula for higher (even) weight modular forms in analytic rank one. Time permitting, I will briefly sketch our strategy of proof of these results. This is joint work (in progress) with Matteo Longo and Daniele Masoero.