Cyclic Isogenies for Abelian Varieties with Real Multiplication
Cyclic Isogenies for Abelian Varieties with Real Multiplication
复制标题
具有实数乘法的阿贝尔簇的循环同基因
DOI：
10.17323/1609-4514-2022-22-4-613-655
复制
发表时间：
2017
影响因子：
0.8
通讯作者：
Marius Vuille
中科院分区：
文献类型：
--
作者：
Alina Dudeanu;Dimitar Jetchev;Damien Robert;Marius Vuille
本文研究了主极化阿贝尔簇与伽罗瓦稳定有限子群的真实的乘法的等价关系，并描述了这些等价关系是主可极化的。我们利用这个特征提供了一个算法来计算显式循环同构的核心交换品种的真实的乘法有限域上。我们的算法是多项式在有限域的大小，以及在程度的ischeros和芒福德的理论的θ函数和θ嵌入的基础上。最近，该算法已被成功地应用于研究亏格2的离散对数问题以及亏格3的离散对数问题。
We study quotients of principally polarized abelian varieties with real multiplication by Galois-stable finite subgroups and describe when these quotients are principally polarizable. We use this characterization to provide an algorithm to compute explicit cyclic isogenies from kernel for abelian varieties with real multiplication over finite fields. Our algorithm is polynomial in the size of the finite field as well as in the degree of the isogeny and is based on Mumford's theory of theta functions and theta embeddings. Recently, the algorithm has been successfully applied to obtain new results on the discrete logarithm problem in genus 2 as well as to study the discrete logarithm problem in genus 3.
通过 2 格曲线的雅可比行列式 (3,3)-同源性下降
影响因子：
0.7
作者：
Bruin N
通讯作者：
Bruin N