2-Selmer groups of hyperelliptic curves with two marked points
Number Theory
2016-11-11 v1
Abstract
We consider the family of hyperelliptic curves over of fixed genus along with a marked rational Weierstrass point and a marked rational non-Weierstrass point. When these curves are ordered by height, we prove that the average Mordell-Weil rank of their Jacobians is bounded above by 5/2. We prove this by showing that the average rank of the 2-Selmer groups is bounded above by 6. We also prove that the average size of the -Selmer groups of a family of isogenies associated to this family is exactly 2.
Keywords
Cite
@article{arxiv.1611.03172,
title = {2-Selmer groups of hyperelliptic curves with two marked points},
author = {Ananth N. Shankar},
journal= {arXiv preprint arXiv:1611.03172},
year = {2016}
}