Reconstruction of one-punctured elliptic curves in positive characteristic by their geometric fundamental groups
Reconstruction of one-punctured elliptic curves in positive characteristic by their geometric fundamental groups
复制标题
正特性单穿刺椭圆曲线的几何基本群重构
DOI：
10.1007/s00229-019-01152-7
复制
发表时间：
2019
影响因子：
0.6
通讯作者：
Akira Sarashina
中科院分区：
文献类型：
--
作者：
武藤奈月;武藤奈月;武藤奈月;Akira Sarashina
我们的主要问题是，作为有限域代数闭包上的曲线X的方案的同构类是否可以通过X的等基本群来重构。当X的属数为0时，玉川对这个问题给出了肯定的回答。本文将讨论属1的情况，并在X的属数为1、尖点基数为1、X的特征不等于2时证明类似的结果。
Our main question is whether the isomorphism class as a scheme of a curveXover an algebraic closure of a finite field can be reconstructed by the etale fundamental group ofX. Tamagawa answered this question affirmatively when the genus ofXis 0. In this paper, we will discuss the genus 1 case, and prove a similar result when the genus ofXis 1, the cardinality of cusps is 1, and the characteristic ofXis not equal to 2.