Galois theory over rings of arithmetic power series

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FEHM, Arno, Elad PARAN, 2011. Galois theory over rings of arithmetic power series. In: Advances in Mathematics. 226(5), pp. 4183-4197. ISSN 0001-8708. Available under: doi: 10.1016/j.aim.2010.11.010

@article{Fehm2011Galoi-14818, title={Galois theory over rings of arithmetic power series}, year={2011}, doi={10.1016/j.aim.2010.11.010}, number={5}, volume={226}, issn={0001-8708}, journal={Advances in Mathematics}, pages={4183--4197}, author={Fehm, Arno and Paran, Elad} }

terms-of-use Fehm, Arno Paran, Elad 2011 Fehm, Arno Paran, Elad 2011-08-17T07:30:33Z Galois theory over rings of arithmetic power series Publ. in: Advances in Mathematics 226 (2011), 5, pp. 4183-4197 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. 2011-08-17T07:30:33Z

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