Doubly isogenous genus-2 curves with 4-action
Doubly isogenous genus-2 curves with 4-action
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具有 4 个作用的双同源 genus-2 曲线
DOI：
10.1090/mcom/3891
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发表时间：
2023
影响因子：
2
通讯作者：
Arul V
中科院分区：
文献类型：
--
作者：
Arul V
我们研究有限域上的曲线在多大程度上是由它们的zeta函数和它们的某些覆盖的zeta函数表征的。假设在有限域上的曲线，具有有理基点和，并且允许（通过Abel-Jacobi映射）对其雅可比矩阵进行逐映射乘法的回调。我们说它们是双重均质，如果它们是上均质和上均质。对于自同构群包含8阶二面体群的属曲线，我们证明了双等同性曲线的对数大于naïve启发式预测，并给出了对这一现象的解释。参考文献
We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Supposeandare curves over a finite field, with-rational base pointsand, and letandbe the pullbacks (via the Abel–Jacobi map) of the multiplication-by-maps on their Jacobians. We say thatandare doubly isogenous ifandare isogenous overandandare isogenous over. For curves of genuswhose automorphism groups contain the dihedral group of order eight, we show that the number of pairs of doubly isogenous curves is larger than naïve heuristics predict, and we provide an explanation for this phenomenon. References