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 | References | Similar Articles | Additional Information
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
