The geometric average size of Selmer groups over function fields

被引：3

作者：

Landesman, Aaron ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

ALGEBRA & NUMBER THEORY | 2021年 / 15卷 / 03期

基金：

美国国家科学基金会;

关键词：

Selmer groups; arithmetic statistics; function fields; moduli stacks; ELLIPTIC-CURVES; STABILITY; PENCILS;

D O I：

10.2140/ant.2021.15.673

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show, in the large q limit, that the average size of n-Selmer groups of elliptic curves of bounded height over F-q(t) is the sum of the divisors of n. As a corollary, again in the large q limit, we deduce that 100% of elliptic curves of bounded height over F-q(t) have rank 0 or 1.

引用

页码：673 / 709

页数：37

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