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The inverse Galois problem over formal power series fields

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Abstract

Consider a valuation ringR of a discrete Henselian field and a positive integerr. LetF be the quotient field of the ringR[[X 1, …,X r ]]. We prove that every finite group occurs as a Galois group overF. In particular, ifK 0 is an arbitrary field andr≥2, then every finite group occurs as a Galois group overK 0((X 1, …,X r )).

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Authors and Affiliations

  1. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Moshe Jarden

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  1. Moshe Jarden
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Correspondence to Moshe Jarden.

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The work on this paper started when the author was an organizer of a research group on the Arithmetic of Fields in the Institute for Advanced Studies at the Hebrew Univesity of Jerusalem in 1991–92. It was partially supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

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Jarden, M. The inverse Galois problem over formal power series fields. Israel J. Math. 85, 263–275 (1994). https://doi.org/10.1007/BF02758644

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  • DOI: https://doi.org/10.1007/BF02758644

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