Diagonal cycles and anticyclotomic twists of modular forms at inert primes

We revisit the construction of Castella and Do of an anticyclotomic Euler system for the $p$-adic Galois representation of a modular form, using diagonal classes. Combining this construction and some previous results of ours, we obtain new results towards the Bloch–Kato conjecture in analytic rank one, assuming that the fixed prime $p$ is inert in the relevant imaginary quadratic field.