The inverse Galois problem over formal power series fields

Moshe Jarden*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Consider a valuation ring R of a discrete Henselian field and a positive integer r. Let F be the quotient field of the ring R[[X 1, ..., X r ]]. We prove that every finite group occurs as a Galois group over F. In particular, if K 0 is an arbitrary field and r≥2, then every finite group occurs as a Galois group over K 0((X 1, ..., X r )).

Original languageEnglish
Pages (from-to)263-275
Number of pages13
JournalIsrael Journal of Mathematics
Volume85
Issue number1-3
DOIs
StatePublished - Feb 1994

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