Curves over every global field violating the local-global principle
classification
🧮 math.NT
math.AG
keywords
fieldglobalcurveeverylocal-globalprincipleviolatingalgorithm
read the original 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.
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