2-SELMER GROUPS OF EVEN HYPERELLIPTIC CURVES OVER FUNCTION FIELDS

被引：0
作者：
Thinh, Dao Van [1 ]
机构：
[1] Peking Univ, BICMR, China 5,Yiheyuan Rd, Beijing 100871, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 07期
关键词：
Hyperelliptic curve; Selmer group; function field; canonical reduction; AVERAGE SIZE; ELLIPTIC-CURVES;
D O I：
10.1090/tran/8878
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we are going to compute the average size of 2-Selmer groups of families of even hyperelliptic curves over function fields. The result will be obtained by a geometric method which is based on a Vinberg's representation of the group G = PSO(2n + 2) and a Hitchin fibration. Consistent with the result over Q of Arul Shankar and Xiaoheng Wang [Compos. Math. 154 (2018), pp. 188-222], we provide an upper bound and a lower bound of the average. However, if we restrict to the family of transversal hyperelliptic curves, we obtain precisely average number 6.
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页码：4679 / 4712
页数：34
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