Existence of rational points on smooth projective varieties
Number Theory
2017-04-03 v1 Algebraic Geometry
Abstract
Fix a number field k. We prove that if there is an algorithm for deciding whether a smooth projective geometrically integral k-variety has a k-point, then there is an algorithm for deciding whether an arbitrary k-variety has a k-point and also an algorithm for computing X(k) for any k-variety X for which X(k) is finite. The proof involves the construction of a one-parameter algebraic family of Chatelet surfaces such that exactly one of the surfaces fails to have a k-point.
Cite
@article{arxiv.0712.1782,
title = {Existence of rational points on smooth projective varieties},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:0712.1782},
year = {2017}
}
Comments
11 pages