Luca Marannino (Jussieu), On anticyclotomic twists of modular forms at inert primes

In this talk, we outline an approach to the study of anticyclotomic twists of modular forms, when the fixed prime p is inert in the relevant quadratic imaginary field. After revisiting old (and less old) results involving Heegner points/cycles, we will focus on our recent work. Following ideas of Castella-Do for the “p split” case, one can envisage a construction of an anticyclotomic Euler system arising from a suitable manipulation of diagonal classes on a triple product of modular curves and obtain new p-adic evidence for the Bloch-Kato conjecture in rank 1 situations.

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