Euler systems for self-dual Hecke characters over biquadratic fields with applications

Source abstract

We construct a new Euler system attached to a self-dual Hecke character $χ$ over an imaginary biquadratic field $K_0$. The Euler system is anticyclotomic in the sense of Jetchev--Neková{\v r}--Skinner. As arithmetic applications, we deduce instances of the Bloch--Kato conjecture in analytic ranks $0$, $1$, and $2$ (the last one for certain CM abelian surfaces). In addition, we establish the full Iwasawa--Greenberg main conjecture for $χ$ over $K_0$. In this biquadratic setting, our work generalizes Rubin's work on the Iwasawa main conjectures for imaginary quadratic fields using Euler systems of elliptic units, while complementing known results of Hida and Hsieh for general CM fields.