A $p$-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties

DOI10.1090/mcom/3029zbMath1402.11099arXiv1210.2739OpenAlexW2146275364WikidataQ122894345 ScholiaQ122894345MaRDI QIDQ2792352

William A. Stein, Jan Steffen Müller, Jennifer S. Balakrishnan

Publication date: 9 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2739

zbMATH Keywords

\(p\)-adic \(L\)-functions\(p\)-adic heights\(p\)-adic BSD conjecture

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Heights (11G50)

Related Items

On pairs of \(p\)-adic \(L\)-functions for weight-two modular forms ⋮ Quadratic Chabauty and 𝑝-adic Gross–Zagier ⋮ Quadratic Chabauty: \(p\)-adic heights and integral points on hyperelliptic curves ⋮ Explicit Vologodsky integration for hyperelliptic curves ⋮ Computing integral points on hyperelliptic curves using quadratic Chabauty ⋮ Explicit quadratic Chabauty over number fields ⋮ Euler characteristics and their congruences in the positive rank setting

Uses Software

• Magma
• SageMath

Cites Work

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