\(p\)-adic Arakelov theory

DOI10.1016/j.jnt.2004.11.010zbMath1079.14033arXivmath/0301029OpenAlexW2033847627MaRDI QIDQ2568213

Amnon Besser

Publication date: 10 October 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301029

zbMATH Keywords

\(p\)-adic integration\(p\)-adic Green functions\(p\)-adic height pairings

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Local ground fields in algebraic geometry (14G20) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (9)

GEOMETRIC QUADRATIC CHABAUTY ⋮ Quadratic Chabauty: \(p\)-adic heights and integral points on hyperelliptic curves ⋮ \(p\)-adic heights and Vologodsky integration ⋮ Explicit Vologodsky integration for hyperelliptic curves ⋮ Computing integral points on hyperelliptic curves using quadratic Chabauty ⋮ The -adic Gross–Zagier formula on Shimura curves ⋮ Vologodsky integration on curves with semi-stable reduction ⋮ Explicit quadratic Chabauty over number fields ⋮ The Syntomic Regulator for K2 of Curves with Arbitrary Reduction

Cites Work

• Calculus on arithmetic surfaces
• Torsion points on curves and p-adic abelian integrals
• \(p\)-adic regulators on curves and special values of \(p\)-adic \(L\)-functions
• The universal vectorial bi-extension and \(p\)-adic heights
• Vectorial extensions of Jacobians
• Universal extensions and one dimensional crystalline cohomology
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Traces and Differential Operators over Beilinson Completion Algebras
• Syntomic regulators and \(p\)-adic integration. II: \(K_2\) of curves
• Coleman integration using the Tannakian formalism
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