Computing canonical heights using arithmetic intersection theory

DOI10.1090/S0025-5718-2013-02719-6zbMath1322.11074arXiv1105.1719OpenAlexW1982362921MaRDI QIDQ2862531

Jan Steffen Müller

Publication date: 15 November 2013

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

Full work available at URL: https://arxiv.org/abs/1105.1719

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) [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)

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 ⋮ A $p$-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties ⋮ Explicit Kummer varieties of hyperelliptic Jacobian threefolds ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing Néron-Tate heights of points on hyperelliptic Jacobians
• Explicit constructions for genus 3 Jacobians
• Calculus on arithmetic surfaces
• Computing the Abel map
• Intersection numbers of sections of elliptic surfaces
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• The Magma algebra system. I: The user language
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• p-adic height pairings. I
• Quasi-functions and heights on abelian varieties
• Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves
• Ueber Korrespondenzen zwischen algebraischen Funktionenkoerpern
• Rational 6-Cycles Under Iteration of Quadratic Polynomials
• Heights and Arakelov's Intersection Theory
• Computing in the Jacobian of a Hyperelliptic Curve
• Computing Heights on Elliptic Curves
• Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
• On the height constant for curves of genus two, II
• Computing Riemann theta functions
• Computing Riemann matrices of algebraic curves
• Factoring polynomials over local fields.

This page was built for publication: Computing canonical heights using arithmetic intersection theory