Anticyclotomic Euler system over biquadratic fields

TL;DR

This paper constructs a new anticyclotomic Euler system for Galois representations associated with modular forms over biquadratic fields and explores its implications for deep conjectures in number theory.

Contribution

It introduces a novel Euler system in the anticyclotomic setting for Galois representations over biquadratic fields, with applications to the Bloch-Kato and Iwasawa-Greenberg conjectures.

Findings

Establishment of an anticyclotomic Euler system for $V_{f,hi}$

Results supporting the Bloch-Kato conjecture in this context

Divisibility results towards the Iwasawa-Greenberg main conjecture

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 $V_{f,\chi}$.