Anti-cyclotomic Euler system of diagonal cycles

Abstract

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

25 pages