Séminaire de Mathématique

# Diagonal Euler systems, p-adic L-functions and the arithmetic of elliptic curves in rank at most 2

## by Prof. Victor ROTGER (Universitat Politècnica de Catalunya, Barcelona)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

ERC Advanced Grant : AAMOT (Arithmetic of Automorphic Motives)

PI : Michael HARRIS

In recent years there has been notable progress on the construction of Euler systems and their connection to special values of classical and p-adic L-functions. In this talk I will describe Euler systems associated to a triple (f,g,h) of classical (cuspidal or Eisenstein) modular forms and their relation with p-adic L-functions constructed by Hida, Harris and Tilouine, following ideas of Kato. As an application, I will explain how these Euler systems can be used to obtain new results on the arithmetic of elliptic curves when the rank of the Mordell-Weil group is 0, 1 or 2.

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