Giada Grossi: Euler systems and the Bloch-Kato conjecture

Since their origins in the works of Thaine and Kolyvagin, Euler systems have been used to produce bounds on certain Selmer groups (e.g. class groups of totally real fields, Tate-Shafarevich groups of rational elliptic curves, etc). Their expected link with $L$-functions has been proved useful to yield some cases of the Birch and Swinnerton-Dyer or the Bloch-Kato conjecture. In this talk, I will give an overview of the theory and the type of tools involved, as well as explain some results about elliptic curves and Hilbert modular forms.