English

Curves over every global field violating the local-global principle

Number Theory 2017-04-03 v2 Algebraic Geometry

Abstract

There is an algorithm that takes as input a global field k and produces a curve over k violating the local-global principle. Also, given a global field k and a nonnegative integer n, one can effectively construct a curve X over k such that #X(k)=n and X has points over every completion of k.

Keywords

Cite

@article{arxiv.0902.3965,
  title  = {Curves over every global field violating the local-global principle},
  author = {Bjorn Poonen},
  journal= {arXiv preprint arXiv:0902.3965},
  year   = {2017}
}

Comments

5 pages

R2 v1 2026-06-21T12:14:35.576Z