Anticyclotomic Euler system over biquadratic fields (2409.19819v1)

Abstract: We construct a new anticyclotomic Euler system (in the sense of Jetchev-Nekovar-Skinner) for the Galois representation $V_{f,\chi}$ attached to a newform $f$ of weight $k\geq 2$ twisted by an anticyclotomic Hecke character $\chi$ defined over an imaginary biquadratic field $K_0$. We then show some arithmetic applications of the constructed Euler system, including results on the Bloch-Kato conjecture, and a divisibility towards the Iwasawa-Greenberg main conjecture for $V_{f,\chi}$.