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.
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页码：615 / 687
页数：73
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