Curves over every global field violating the local-global principle

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.

5 pages

References in corpus (4)

• Existence of rational points on smooth projective varieties
• First-order definitions in function fields over anti-Mordellic fields
• Failure of the Hasse principle for Chatelet surfaces in characteristic 2
• Curves over global fields violating the Hasse Principle

Cited by in corpus (1)

• Curves over global fields violating the Hasse Principle