Anticyclotomic Euler system over biquadratic fields

2024/09/29 by Do, Kim Tuan
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.19819

Abstract

We construct a new Euler system (anticyclotomic, in the sense of Jetchev-Nekovar-Skinner) for the Galois representation V_f,χ attached to a newform f of weight k≥ 2 twisted by an anticyclotomic Hecke character χ defined over an imaginary biquadratic field K₀. 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.

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