2-Selmer groups of even hyperelliptic curves over function fields
Number Theory
2018-11-27 v1
Abstract
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 representation of the group and a Hitchin fibration. Consistent with the result over Q of Arul Shankar and Xiaoheng Wang [Rational points on hyperelliptic curves having a marked non-Weierstrass point, in Compos. Math., 154(1):188-222, 2018], 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 number 6.
Keywords
Cite
@article{arxiv.1811.10539,
title = {2-Selmer groups of even hyperelliptic curves over function fields},
author = {Dao Van Thinh},
journal= {arXiv preprint arXiv:1811.10539},
year = {2018}
}