Three counterexamples concerning the Northcott property of fields

2017/08/22 by Arno Fehm, Fehm, Arno
Mathematics · #11G50 #12E25 #12F10 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G50 #msc:12E25 #msc:12F10

paper · pdf · doi:10.48550/arxiv.1708.06599

5 pages

arxiv created 2017/08/22 · arxiv updated 2017/08/23

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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