On the Tamagawa number conjecture for motives of modular forms

 I plan to present a work in collaboration with Stefano Vigni, in which we study the Tamagawa number conjecture, formulated by Bloch-Kato, in the case of motives attached to cuspforms. This conjecture can be seen as a generalisation to motives of the Birch and Swinnerton-Dyer conjecture for elliptic curves, and is still wide open. The case of motives of modular forms can be studied using methods analogous to those exploited in the case of elliptic curves. After an introduction in which I will recall the main results in the case of elliptic curves, I will discuss our results in the case of motives of modular forms.