Eisenstein congruences among Euler systems

We investigate Eisenstein congruences between the so-called Euler systems of Garrett–Rankin–Selberg type. This includes the cohomology classes of Beilinson–Kato, Beilinson–Flach and diagonal cycles. The proofs crucially rely on different known versions of the Bloch–Kato conjecture, and are based on the study of the Perrin-Riou formalism and the comparison between the different $p$-adic $L$-functions.