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arXiv · 2005.10609

On the Northcott property and local degrees

Sara Checcoli·Arno Fehm
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Abstract

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

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Sara Checcoli, Arno Fehm. 2020-05-21. On the Northcott property and local degrees. https://arxiv.org/abs/2005.10609

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