E6 AND THE ARITHMETIC OF A FAMILY OF NON-HYPERELLIPTIC CURVES OF GENUS 3

被引：11

作者：

Thorne, Jack A. ^{[1
]}

机构：

[1] DPMMS, Cambridge CB3 0WB, England

来源：

FORUM OF MATHEMATICS PI | 2015年 / 3卷

关键词：

D O I：

10.1017/fmp.2014.2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the arithmetic of a family of non-hyperelliptic curves of genus 3 over the field Q of rational numbers. These curves are the nearby fibers of the semi-universal deformation of a simple singularity of type E-6. We show that average size of the 2-Selmer sets of these curves is finite (if it exists). We use this to show that a positive proposition of these curves (when ordered by height) has integral points everywhere locally, but no integral points globally.

引用

页数：41

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