Academic Journal
Computing isogenies from modular equations in genus two
| Title: | Computing isogenies from modular equations in genus two |
|---|---|
| Authors: | Jean Kieffer, Aurel Page, Damien Robert |
| Contributors: | Kieffer, Jean |
| Source: | Journal of Algebra. 666:331-386 |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Algorithm, Mathematics - Algebraic Geometry, Mathematics - Number Theory, Modular equations, Isogenies, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, Number Theory (math.NT), Abelian surfaces, 0101 mathematics, 01 natural sciences, Algebraic Geometry (math.AG), [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] |
| Description: | We present an algorithm solving the following problem: given two genus 2 curves over a field k with isogenous Jacobians, compute such an isogeny explicitly. This isogeny can be either an l-isogeny or, in the real multiplication case, an isogeny with cyclic kernel; we require that k have large enough characteristic and that the curves be sufficiently generic. Our algorithm uses modular equations for these isogeny types, and makes essential use of an explicit Kodaira--Spencer isomorphism in genus 2. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2024.11.029 |
| DOI: | 10.48550/arxiv.2001.04137 |
| Access URL: | http://arxiv.org/abs/2001.04137 https://hal.science/hal-02436133v3/document https://hal.science/hal-02436133v3 https://doi.org/10.1016/j.jalgebra.2024.11.029 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....ff4601e4ed6db61cfbc6afc78bfc12f9 |
| Database: | OpenAIRE |
| ISSN: | 00218693 |
|---|---|
| DOI: | 10.1016/j.jalgebra.2024.11.029 |