Computing isogenies between Jacobian of curves of genus 2 and 3

Autor:	Milio, Enea
Přispěvatelé:	Milio, Enea
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Mathematics::Number Theory FOS: Mathematics [MATH] Mathematics [math] Algebraic Geometry (math.AG) Mathematics::Geometric Topology
Popis:	We present a quasi-linear algorithm to compute isogenies between Jacobians of curves of genus 2 and 3 starting from the equation of the curve and a maximal isotropic subgroup of the l-torsion, for l an odd prime number, generalizing the V\'elu's formula of genus 1. This work is based from the paper "Computing functions on Jacobians and their quotients" of Jean-Marc Couveignes and Tony Ezome. We improve their genus 2 case algorithm, generalize it for genus 3 hyperelliptic curves and introduce a way to deal with the genus 3 non-hyperelliptic case, using algebraic theta functions. Comment: 34 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db8ec54ccd49ef7cc59e39702678fd18 https://hal.science/hal-01589683v2 Zobrazit plný text záznamu