PreprintCC BY 4.0arXiv
Euler systems for self-dual Hecke characters over biquadratic fields with applications
Abstract
We construct a new Euler system attached to a self-dual Hecke character χ over an imaginary biquadratic field K0. 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 K0. 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.
Related
- An infinite family of imaginary biquadratic fields with a large class number
- On real biquadratic number fields for which the $2$-Iwasawa module has rank $3$
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- Hypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fields
- Extreme values of Euler-Kronecker constants of abelian cubic fields
BibTeX
@misc{do2026euler,
title = {{Euler systems for self-dual Hecke characters over biquadratic fields with applications}},
author = {Kim Tuan Do},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28196},
eprint = {2610.28196},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28196},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Euler systems for self-dual Hecke characters over biquadratic fields with applications
AU - Kim Tuan Do
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28196
UR - https://arxiv.org/abs/2610.28196
AB - 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.
ER -