Publikation: Galois theory over rings of arithmetic power series
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2011
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Paran, Elad
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Advances in Mathematics. 2011, 226(5), pp. 4183-4197. ISSN 0001-8708. Available under: doi: 10.1016/j.aim.2010.11.010
Zusammenfassung
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.
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510 Mathematik
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FEHM, Arno, Elad PARAN, 2011. Galois theory over rings of arithmetic power series. In: Advances in Mathematics. 2011, 226(5), pp. 4183-4197. ISSN 0001-8708. Available under: doi: 10.1016/j.aim.2010.11.010BibTex
@article{Fehm2011Galoi-14818,
year={2011},
doi={10.1016/j.aim.2010.11.010},
title={Galois theory over rings of arithmetic power series},
number={5},
volume={226},
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journal={Advances in Mathematics},
pages={4183--4197},
author={Fehm, Arno and Paran, Elad}
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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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