Some cases of the Bloch-Kato conjecture for four-dimensional symplectic Galois representations

The Bloch-Kato conjecture is a far-reaching generalization of the famous conjecture of Birch and Swinnerton-Dyer on L functions of elliptic curves. This talk is about recent results towards Bloch-Kato in rank 0 and 1 for spin L-functions of certain automorphic representations of $\operatorname{GSp}_4$. I’ll explain the statements and some ideas of the proof, which is based on constructing ramified Galois cohomology classes via level-raising congruences.