Anticyclotomic Euler system over biquadratic fields

Abstract

We construct a new Euler system (anticyclotomic, 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 $V_{f,\chi}$.