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}
}
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5 pages