The geometric distribution of Selmer groups of elliptic curves over function fields

被引：2

作者：

Feng, Tony ^{[1
]}

Landesman, Aaron ^{[2
]}

Rains, Eric M. ^{[3
]}

机构：

[1] Univ Calif Berkeley, Berkeley, CA 94720 USA

[2] Harvard Univ, Cambridge, MA 02138 USA

[3] CALTECH, Pasadena, CA 91125 USA

来源：

MATHEMATISCHE ANNALEN | 2023年 / 387卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

AVERAGE SIZE; MONODROMY; RANKS;

D O I：

10.1007/s00208-022-02429-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fix a positive integer n and a finite field F-q. We study the joint distribution of the rank rk(E), the n-Selmer group Sel(n)(E), and the n-torsion in the Tate-Shafarevich group III (E)[n] as E varies over elliptic curves of fixed height d >= 2 over F-q(t). We compute this joint distribution in the large q limit. We also show that the "large q, then large height" limit of this distribution agrees with the one predicted by Bhargava-Kane-Lenstra-Poonen-Rains.

引用

页码：615 / 687

页数：73

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