Canonical heights on the Jacobians of curves of genus 2 and the infinite descent

DOI10.4064/aa-79-4-333-352zbMath0895.11026OpenAlexW1533469128MaRDI QIDQ4345817

E. Victor Flynn, Nigel P. Smart

Publication date: 29 July 1997

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/206982

zbMATH Keywords

algorithmMordell-Weil groupcurves of genus twoJacobianscanonical heightinfinite descent

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) [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)]

Related Items (15)

An Explicit Theory of Heights for Hyperelliptic Jacobians of Genus Three ⋮ Lower bound of the Néron-Tate height on abelian surfaces ⋮ On an analogue of the Lutz-Nagell theorem for hyperelliptic curves ⋮ Computing Néron-Tate heights of points on hyperelliptic Jacobians ⋮ Traces of the group law on the Kummer surface of a curve of genus 2 in characteristic 2 ⋮ Computing integral points on hyperelliptic curves using quadratic Chabauty ⋮ Computing torsion subgroups of Jacobians of hyperelliptic curves of genus 3 ⋮ Rational points on curves ⋮ Computing integral points on genus 2 curves estimating hyperelliptic logarithms ⋮ Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves ⋮ Computing unit groups of curves ⋮ The Hasse principle and the Brauer-Manin obstruction for curves ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights ⋮ Décompositions en hauteurs locales ⋮ Computing canonical heights using arithmetic intersection theory

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