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

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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 andp-adicL-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 withp-adicL-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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