Anti-cyclotomic Euler system of diagonal cycles

We construct split anti-cyclotomic Euler systems for Galois representations attached to certain RACSDC automorphic representations on the group ${\mathrm{G}\mathrm{L}}_n\times {\mathrm{G}\mathrm{L}}_{n+1}$. As a result, we make progress towards certain rank 1 cases of the Beilinson–Bloch–Kato conjecture for those representations.