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arXiv · 0712.1782

Existence of rational points on smooth projective varieties

Bjorn Poonen
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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.

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BibTeXRIS

Bjorn Poonen. 2007-12-11. Existence of rational points on smooth projective varieties. https://doi.org/10.4171/jems%2F159

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