超特殊曲线的同构类计数
代数几何
2021-10-04 v2 数论
摘要
超特殊曲线是定义于正特征域上的(非奇异)曲线,其雅可比簇同构于超奇异椭圆曲线在代数闭包上的乘积。已知对给定的亏格与特征,在同构意义下(在代数闭域上)仅存在有限多个超特殊曲线。本文中,我们简要综述超特殊曲线同构类计数的相关结果。特别地,本文总结了作者与 S. Harashita 近期在亏格四与亏格五情形的一些结果。我们还综述了与 Harashita 及 E. W. Howe 合作工作中,关于一类特定非超椭圆亏格四曲线中超特殊曲线枚举的结果。
引用
@article{arxiv.2106.12409,
title = {Counting isomorphism classes of superspecial curves},
author = {Momonari Kudo},
journal= {arXiv preprint arXiv:2106.12409},
year = {2021}
}
备注
This is the write-up of a lecture delivered 14 October 2020 in the conference supersingular2020 at RIMS, Kyoto. Title has been slightly changed. To appear in RIMS Kokyuroku Bessatsu (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)