Wojciech J. Gajda

Given an elliptic curve E over Q_p, understanding the Galois action on the l-power torsion is central to understanding the arithmetic of E itself via tools such as L-functions. I will briefly survey the classical l/=p setting which is well understood before focusing on one aspect of the harder l=p setting. Here we can now produce concrete statements from the otherwise notoriously abstract realm of p-adic Hodge theory. This is joint work with Lorenzo Furio and Davide Lombardo.