Type of Publication:  Journal article 
Author:  Fehm, Arno; Paran, Elad 
Year of publication:  2011 
Published in:  Advances in Mathematics ; 226 (2011), 5.  pp. 41834197.  ISSN 00018708 
DOI (citable link):  https://dx.doi.org/10.1016/j.aim.2010.11.010 
Summary: 
Let R be a domain, complete with respect to a norm which defines a nondiscrete 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 semifree. This strengthens a theorem of Harbater, who solved the inverse Galois problem over these fields.

Subject (DDC):  510 Mathematics 
Bibliography of Konstanz:  Yes 
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FEHM, Arno, Elad PARAN, 2011. Galois theory over rings of arithmetic power series. In: Advances in Mathematics. 226(5), pp. 41834197. ISSN 00018708. Available under: doi: 10.1016/j.aim.2010.11.010
@article{Fehm2011Galoi14818, title={Galois theory over rings of arithmetic power series}, year={2011}, doi={10.1016/j.aim.2010.11.010}, number={5}, volume={226}, issn={00018708}, journal={Advances in Mathematics}, pages={41834197}, author={Fehm, Arno and Paran, Elad} }