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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Northcott property and local degrees
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by S. Checcoli and A. Fehm
Proc. Amer. Math. Soc. 149 (2021), 2403-2414
DOI: https://doi.org/10.1090/proc/15411
Published electronically: March 26, 2021

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.
References
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Bibliographic 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
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2403-2414
  • MSC (2020): Primary 11G50, 12E30, 11R04, 12F05
  • DOI: https://doi.org/10.1090/proc/15411
  • MathSciNet review: 4246793