Special cycles on Shimura varieties for U(n,1)xU(n-1,1) and the Bloch-Kato conjecture for conjugate-dual Galois representations

Using a recently constructed Euler system of special cycles on unitary groups, we show how to obtain new results towards the Bloch-Kato conjecture for conjugate-dual Galois representations appearing in the middle-degree cohomology of the ambient unitary Shimura variety. In addition, we explain how to use recent vertical norm-compatibility result due to Boumasmoud, Brooks and Jetchev in order to obtain novel anticyclotomic Iwasawa-theoretic results.