Anticyclotomic Euler system over biquadratic fields

Do, Kim Tuan

doi:10.2140/ant.2026.20.1615

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Anticyclotomic Euler system over biquadratic fields

Kim Tuan Do

Vol. 20 (2026), No. 8, 1615–1647

DOI: 10.2140/ant.2026.20.1615

Abstract

We construct a new Euler system (anticyclotomic, in the sense of Jetchev–Nekovář–Skinner) for the Galois representation $V_{f, χ}$ attached to a newform $f$ of weight $k \geq 2$ twisted by an anticyclotomic Hecke character $χ$ 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 $V_{f, χ}$ .

Keywords

Euler system, Bloch–Kato conjecture, Iwasawa theory, Selmer groups

Mathematical Subject Classification

Primary: 11F67, 11R23

Milestones

Received: 30 September 2024

Revised: 5 May 2025

Accepted: 1 July 2025

Published: 25 September 2026

Authors

Kim Tuan Do
Department of Mathematics University of California, Los Angeles Los Angeles, CA United States	Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States

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Vol. 20, No. 8, 2026