论文标题
来自属的模块化方程的计算同源物
Computing isogenies from modular equations in genus two
论文作者
论文摘要
我们提出了解决以下问题的算法：给定两种属2曲线，具有同源性雅各布人的场k，明确计算出这样的同等基因。 这种同性基因可以是L-异构体，也可以是实际乘法的情况，是带有环状核的同性基因。我们要求k具有足够大的特性，并且曲线足够通用。 我们的算法使用模块化方程来对这些同等类型类型，并在2属中对显式kodaira-spencer同构的必不可少。
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.
