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On the Northcott property and local degrees


Authors: S. Checcoli and A. Fehm
Journal: Proc. Amer. Math. Soc. 149 (2021), 2403-2414
MSC (2020): Primary 11G50, 12E30, 11R04, 12F05
DOI: https://doi.org/10.1090/proc/15411
Published electronically: March 26, 2021
MathSciNet review: 4246793
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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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Additional Information

S. Checcoli
Affiliation: Institut Fourier, Université Grenoble Alpes, 100 rue des Mathématiques, 38610 Gières, France
MR Author ID: 924817
Email: sara.checcoli@univ-grenoble-alpes.fr

A. Fehm
Affiliation: Institut für Algebra, Fakultät Mathematik, Technische Universität Dresden, 01062 Dresden, Germany
MR Author ID: 887431
ORCID: 0000-0002-2170-9110
Email: arno.fehm@tu-dresden.de

Received by editor(s): June 9, 2020
Received by editor(s) in revised form: September 30, 2020, and October 26, 2020
Published electronically: March 26, 2021
Additional Notes: The first author’s work was funded by the ANR project Gardio 14-CE25-0015
The second author was funded by the Deutsche Forschungsgemeinschaft (DFG) - 404427454
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2021 American Mathematical Society