Towards the Bloch-Kato conjecture for spin L-functions on GSp4

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 zero and one for spin L-functions of certain automorphic representations of GSp₄. I'll explain the statements and some ideas of the proof, which is based on constructing ramified Galois cohomology classes via level-raising congruences.