English

On genus one curves violating the local-global principle

Number Theory 2022-03-03 v2

Abstract

For any number field not containing \QQ(i),\QQ(i), we give an explicit construction to prove that there exists an elliptic curve defined over this field such that its Shafarevich-Tate group is nontrivial.

Keywords

Cite

@article{arxiv.2112.02470,
  title  = {On genus one curves violating the local-global principle},
  author = {Han Wu},
  journal= {arXiv preprint arXiv:2112.02470},
  year   = {2022}
}
R2 v1 2026-06-24T08:04:34.459Z