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arXiv · 1708.06599

Three counterexamples concerning the Northcott property of fields

Arno Fehm
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Abstract

We give three examples of fields concerning the Northcott property on elements of small height: The first one has the Northcott property but its Galois closure does not satisfy the Bogomolov property. The second one has the Northcott property and is pseudo-algebraically closed, i.e. every variety has a dense set of rational points. The third one has bounded local degree at infinitely many rational primes but does not have the Northcott property.

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Arno Fehm. 2017-08-22. Three counterexamples concerning the Northcott property of fields. https://arxiv.org/abs/1708.06599

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