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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The local dimension of a finite group over a number field
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by Joachim König and Danny Neftin PDF
Trans. Amer. Math. Soc. 375 (2022), 4783-4808 Request permission


Let $G$ be a finite group and $K$ a number field. We construct a $G$-extension $E/F$, with $F$ of transcendence degree $2$ over $K$, that specializes to all $G$-extensions of $K_\mathfrak {p}$, where $\mathfrak {p}$ runs over all but finitely many primes of $K$. If furthermore $G$ has a generic extension over $K$, we show that the extension $E/F$ has the so-called Hilbert–Grunwald property. These results are compared to the notion of essential dimension of $G$ over $K$, and its arithmetic analogue.
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Additional Information
  • Joachim König
  • Affiliation: Department of Mathematics Education, Korea National University of Education, Cheongju, South Korea
  • ORCID: 0000-0003-0008-3283
  • Danny Neftin
  • Affiliation: Department of Mathematics, Technion - IIT, Haifa, Israel
  • ORCID: 0000-0003-4731-8422
  • Received by editor(s): August 8, 2020
  • Received by editor(s) in revised form: July 27, 2021, and November 14, 2021
  • Published electronically: April 21, 2022
  • Additional Notes: The first and second author were supported by the National Research Foundation of Korea (grant no. 2019 R1C1C1002665) and the Israel Science Foundation (grants no. 577/15 and 353/21), respectively
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 4783-4808
  • MSC (2020): Primary 11R32; Secondary 14H30, 14G05, 11S20
  • DOI:
  • MathSciNet review: 4439491