2-Selmer near-companion curves

Myungjun Yu

2-Selmer near-companion curves

Number Theory 2016-11-09 v2

Authors: Myungjun Yu

Abstract

Let $E$ and $A$ be elliptic curves over a number field $K$ . Let $\chi$ be a quadratic character of $K$ . We prove the conjecture posed by Mazur and Rubin on $n$ -Selmer near-companion curves in the case $n=2$ . Namely, we show if the difference of the $2$ -Selmer ranks of $E^\chi$ and $A^\chi$ is bounded independent of $\chi$ , there is a $G_K$ -isomorphism $E[2] \cong A[2]$ .

Keywords

elliptic curves Selmer group near-companion curves quadratic character Mazur-Rubin conjecture Galois isomorphism number field

Cite

@article{arxiv.1610.01195,
  title  = {2-Selmer near-companion curves},
  author = {Myungjun Yu},
  journal= {arXiv preprint arXiv:1610.01195},
  year   = {2016}
}

Comments

16 pages

Related papers

View all related →