English

On the Northcott property and local degrees

Number Theory 2020-06-03 v2

Abstract

We construct infinite Galois extensions KK of Q\mathbb{Q} that satisfy the Northcott property on elements of small height, and where this property can be deduced solely from the splitting behavior of prime numbers in KK. We also give examples of Galois extensions of Q\mathbb{Q} which have finite local degree at all prime numbers and do not satisfy the Northcott property.

Keywords

Cite

@article{arxiv.2005.10609,
  title  = {On the Northcott property and local degrees},
  author = {Sara Checcoli and Arno Fehm},
  journal= {arXiv preprint arXiv:2005.10609},
  year   = {2020}
}

Comments

strengthened Theorem 1.2, added remarks on undecidability results

R2 v1 2026-06-23T15:42:52.218Z