ANNULÉ/CANCEL - Structural refinements of Birch and Swinnerton-Dyer conjecture and Gross-Zagier formula

Abstract: We discuss refined applications of (a part of) the Iwasawa main conjecture for elliptic curves to the non-triviality of Kato's Kolyvagin systems and the structure of Selmer groups of elliptic curves of arbitrary rank. The former is the cyclotomic version of Kolyvagin's conjecture and the latter can be viewed as a structural refinement of Birch and Swinnerton-Dyer conjecture. Using the result on the structure of Selmer groups, we are able to compare directly the collection of Kurihara numbers, which is the modular symbol version of Kato's Kolyvagin systems, with Heegner point Kolyvagin systems. This comparison itself can be regarded as a structural refinement of Gross-Zagier formula from the viewpoint of Kolyvagin systems.

number theory

Audience: researchers in the topic

CRM-CICMA Québec Vermont Seminar Series

Series comments: En ligne/Web - Pour information, veuillez communiquer à / For details, please contact: activités@crm.umontreal.ca