Computing Néron-Tate heights of points on hyperelliptic Jacobians

DOI10.1016/j.jnt.2012.01.002zbMath1239.14019arXiv1004.4503OpenAlexW1994992566MaRDI QIDQ413427

David Holmes

Publication date: 7 May 2012

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

Full work available at URL: https://arxiv.org/abs/1004.4503

zbMATH Keywords

hyperelliptic curveNéron-Tate heightArakelov theorycanonical height

Mathematics Subject Classification ID

[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) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Related Items (9)

An Explicit Theory of Heights for Hyperelliptic Jacobians of Genus Three ⋮ Numerical Verification of the Birch and Swinnerton-Dyer Conjecture for Hyperelliptic Curves of Higher Genus over ℚ up to Squares ⋮ Canonical heights and division polynomials ⋮ Explicit Vologodsky integration for hyperelliptic curves ⋮ Quadratic Chabauty for modular curves: algorithms and examples ⋮ Computing unit groups of curves ⋮ Explicit Kummer varieties of hyperelliptic Jacobian threefolds ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights ⋮ Computing canonical heights using arithmetic intersection theory

Uses Software

• Magma

Cites Work

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• Heights and Arakelov's Intersection Theory
• Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura

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