Quadratic Chabauty: \(p\)-adic heights and integral points on hyperelliptic curves

DOI10.1515/crelle-2014-0048zbMath1350.11067arXiv1302.2944OpenAlexW2963968797MaRDI QIDQ334476

Amnon Besser, Jennifer S. Balakrishnan, Jan Steffen Müller

Publication date: 1 November 2016

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2944

zbMATH Keywords

rational pointsheightsArakelov theoryarithmetic varieties and schemescurves of arbitrary genus or genus \(\neq 1\) over global fields

Mathematics Subject Classification ID

Rational points (14G05) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

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Uses Software

• Magma
• SageMath

Cites Work

• Explicit Chabauty over number fields
• Coleman-Gross height pairings and the \(p\)-adic sigma function
• Selmer varieties for curves with CM Jacobians
• \(p\)-adic \(L\)-functions and Selmer varieties associated to elliptic curves with complex multiplication
• Integral points on hyperelliptic curves
• The unipotent Albanese map and Selmer varieties for curves
• Torsion points on curves and p-adic abelian integrals
• Effective Chabauty
• Duality for the de Rham cohomology of an abelian scheme
• The Magma algebra system. I: The user language
• A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves
• The syntomic regulator for \(K_4\) of curves
• An Arakelov-theoretic approach to naïve heights on hyperelliptic Jacobians
• Computation of \(p\)-adic heights and log convergence
• Canonical heights on genus-2 Jacobians
• The complete classification of fibres in pencils of curves of genus two
• \(p\)-adic Arakelov theory
• The motivic fundamental group of \(\mathbf P^1\setminus\{0,1,\infty\}\) and the theorem of Siegel
• Vologodsky integration on curves with semi-stable reduction
• Implementing 2-descent for Jacobians of hyperelliptic curves
• A $p$-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
• Computing Local p-adic Height Pairings on Hyperelliptic Curves
• Appendix and erratum to “Massey products for elliptic curves of rank 1”
• Efficient Computation of p-Adic Heights
• Massey products for elliptic curves of rank 1
• On the height constant for curves of genus two, II
• An Explicit Theory of Heights for Hyperelliptic Jacobians of Genus Three
• Explicit Coleman Integration for Hyperelliptic Curves
• Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces
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