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arXiv:1708.06599 [math.NT]AbstractReferencesReviewsResources

Three counterexamples concerning the Northcott property of fields

Arno Fehm

Published 2017-08-22Version 1

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.

Comments: 5 pages
Categories: math.NT
Subjects: 11G50, 12E25, 12F10
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