Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Do, Kim Tuan
Institution: University of California, Santa Barbara
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223087206