Curves over every global field violating the local-global principle

Details Curves over every global field violating the local-global principle Curves over every global field violating the local-global principle

2009-02-23

arxiv.org/abs/0902.3965v2

Mathematics

Number Theory

5 pages

Scientific paper

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.

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