On the Northcott property and local degrees

Checcoli, S.; Fehm, A.

doi:10.1090/proc/15411

On the Northcott property and local degrees
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by S. Checcoli and A. Fehm PDF

Proc. Amer. Math. Soc. 149 (2021), 2403-2414 Request permission

Abstract:

We construct infinite Galois extensions $L$ of $\mathbb {Q}$ that satisfy the Northcott property on elements of small height, and where this property can be deduced solely from the local behavior of $L$ at the different prime numbers. 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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