Euler systems, the Birch–Swinnerton-Dyer conjecture and the structure of Selmer groups

Some results about arithmetic of elliptic curves related to the method of Euler systems will be discussed. In particular, the recent developments in proving of non vanishing properties of cohomology classes obtained from the Euler system of Heegner points and their applications to the Birch–Swinnerton-Dyer conjecture and the study of Selmer groups will be discussed.