Diagonal cycles and anticyclotomic twists of modular forms at inert primes

We revisit the construction of Castella–Do [8] of an anticyclotomic Euler system for the p-adic Galois representation of a modular form, using diagonal classes. Combining this construction and some of the results of our previous work [18], we obtain new results toward the Bloch–Kato conjecture in analytic rank one, assuming that the fixed prime p is inert in the relevant imaginary quadratic field.