SEMINARIO TEORÍA DE NÚMEROS

Title: QUATERNIONIC KOLYVAGIN SYSTEMS AND IWASAWA THEORY FOR HIDA FAMILIES

SPEAKER: Francesco Zerman (University of Genova)

DATE & TIME: Miércoles 21 de febrero - 12:30

VENUE: Aula 420, Departamento de Matemáticas, UAM.

ABSTRACT: The goal of this talk is to present the work for my Ph.D. thesis, that consists in the construction of a Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system built by Longo and Vigni in towers of Shimura curves. We generalize a work of Buyukbokuk to a quaternionic setting, relaxing the classical Heegner hypothesis on the tame conductor of the family. As a byproduct of this construction, we give a proof of one divisibility of the anticyclotomic Iwasawa main conjecture for Hida families. In order to make the talk more digestible, we will always try to underline the parallelisms and the motivation coming from the realm of elliptic curves.