On the Northcott property and local degrees

2020/05/21 by Sara Checcoli, Arno Fehm, Checcoli, Sara +1 · 1 citation
Mathematics · #11G50 #11R04 #12E30 #12F05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G50 #msc:11R04 #msc:12E30 #msc:12F05

paper · pdf · doi:10.48550/arxiv.2005.10609

strengthened Theorem 1.2, added remarks on undecidability results

arxiv created 2020/06/02 · arxiv updated 2020/06/03

Abstract

We construct infinite Galois extensions K of 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 K. We also give examples of Galois extensions of ℚ which have finite local degree at all prime numbers and do not satisfy the Northcott property.

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