Galois theory over rings of arithmetic power series

Fehm, Arno; Paran, Elad

Galois theory over rings of arithmetic power series

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Datum

2011

Autor:innen

Fehm, Arno

Paran, Elad

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

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.

Fachgebiet (DDC)

510 Mathematik

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ISO 690

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.2010.11.010

BibTex

@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},
  issn={0001-8708},
  journal={Advances in Mathematics},
  pages={4183--4197},
  author={Fehm, Arno and Paran, Elad}
}

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