Anti-cyclotomic Euler system of diagonal cycles

TL;DR

This paper constructs anti-cyclotomic Euler systems for specific Galois representations, advancing the understanding of the Beilinson--Bloch--Kato conjecture in rank 1 cases.

Contribution

It introduces a new construction of split anti-cyclotomic Euler systems for automorphic Galois representations on GL(n)×GL(n+1).

Findings

Progress towards rank 1 cases of the Beilinson--Bloch--Kato conjecture.

Construction of Euler systems for automorphic Galois representations.

Enhancement of tools for studying special values of L-functions.

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.