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arXiv · 2507.22755

Diagonal cycles and anticyclotomic twists of modular forms at inert primes

Luca Marannino
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Abstract

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.

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Luca Marannino. 2025-07-30. Diagonal cycles and anticyclotomic twists of modular forms at inert primes. https://arxiv.org/abs/2507.22755

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