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)

Tuesday Jan 17, 2017, 11:30 AM → 12:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.