Three counterexamples concerning the Northcott property of fields

  • Arno Fehm

    Technische Universität Dresden, Germany

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 even 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 this article

Arno Fehm, Three counterexamples concerning the Northcott property of fields. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 2, pp. 309–314

DOI 10.4171/RLM/807