English

Three counterexamples concerning the Northcott property of fields

Number Theory 2017-08-23 v1

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.

Cite

@article{arxiv.1708.06599,
  title  = {Three counterexamples concerning the Northcott property of fields},
  author = {Arno Fehm},
  journal= {arXiv preprint arXiv:1708.06599},
  year   = {2017}
}

Comments

5 pages

R2 v1 2026-06-22T21:20:29.896Z