2021/12/31 by Joachim König, König, Joachim, Danny Neftin +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2112.15467
openalex publication_date 2021/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.