Derived Bockstein regulators and anticyclotomic p-adic Birch and Swinnerton-Dyer conjectures

2023/08/17 by Takamichi Sano, Sano, Takamichi · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2308.08875

openalex publication_date 2023/08/17 · openalex created_date 2023/08/22 · openalex updated_date 2026/07/28

Abstract

We introduce "derived Bockstein regulators" by using an idea of Nekovář. We establish a general descent formalism involving derived Bockstein regulators. We give three applications of this formalism. Firstly, we show that a conjecture of Birch and Swinnerton-Dyer type for Heegner points formulated by Bertolini and Darmon in 1996 follows from Perrin-Riou's Heegner point main conjecture up to a p-adic unit. Secondly, we show that a p-adic Birch and Swinnerton-Dyer conjecture for the Bertolini-Darmon-Prasanna p-adic L-function recently formulated by Agboola and Castella follows from the Iwasawa-Greenberg main conjecture up to a p-adic unit. Finally, we extend conjectures and results on derivatives of Euler systems for a general motive given by Kataoka and the present author into a natural derived setting.

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