On the Northcott property and local degrees
Number Theory
2020-06-03 v2
Abstract
We construct infinite Galois extensions of 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 . We also give examples of Galois extensions of 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