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The Hilbert–Grunwald specialization property over number fields

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Abstract

Given a finite group G and a number field K, we investigate the following question: Does there exist a Galois extension E/K(t) with group G whose set of specializations yields solutions to all Grunwald problems for the group G, outside a finite set of primes? Following previous work, such a Galois extension would be said to have the “Hilbert–Grunwald property”. In this paper we reach a complete classification of groups G which admit an extension with the Hilbert–Grunwald property over fields such as K = ℚ. We thereby also complete the determination of the “local dimension” of finite groups over ℚ.

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Authors and Affiliations

  1. Department of Mathematics Education, Korea National University of Education, Chungbuk, 28173, Republic of Korea

    Joachim König

  2. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Danny Neftin

Authors
  1. Joachim König
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  2. Danny Neftin
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Correspondence to Joachim König.

Additional information

Dedicated to Moshe Jarden on the occasion of his 80th birthday

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König, J., Neftin, D. The Hilbert–Grunwald specialization property over number fields. Isr. J. Math. 257, 433–463 (2023). https://doi.org/10.1007/s11856-023-2538-0

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  • DOI: https://doi.org/10.1007/s11856-023-2538-0

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