Galois theory over rings of arithmetic power series

Arno Fehm, Elad Paran

Research output: Contribution to journalArticlepeer-review


Let R be a domain, complete with respect to a norm which defines a non-discrete topology on R. We prove that the quotient field of R is ample, generalizing a theorem of Pop. We then consider the case where R is a ring of arithmetic power series which are holomorphic on the closed disc of radius 0<r<1 around the origin, and apply the above result to prove that the absolute Galois group of the quotient field of R is semi-free. This strengthens a theorem of Harbater, who solved the inverse Galois problem over these fields.

Original languageEnglish
Pages (from-to)4183-4197
Number of pages15
JournalAdvances in Mathematics
Issue number5
StatePublished - 20 Mar 2011
Externally publishedYes

Bibliographical note

Funding Information:
The first author was supported by the European Commission under contract MRTN-CT-2006-035495. The second author was supported by an ERC grant.

Copyright 2011 Elsevier B.V., All rights reserved.


  • Ample fields
  • Galois theory
  • Large fields
  • Power series
  • Semi-free profinite groups
  • Split embedding problems


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