Small Galois groups that encode valuations

Ido Efrat; Jan Minac

Small Galois groups that encode valuations

Number Theory 2011-12-16 v2

Authors: Ido Efrat , Jan Minac

Abstract

Let $p$ be a prime number and let $F$ be a field containing a root of unity of order $p$ . We prove that a certain very small canonical Galois group $(G_F)_{[3]}$ over $F$ encodes the valuations on $F$ whose value group is not $p$ -divisible and which satisfy a variant of Hensel's lemma.

Keywords

galois theory finite groups representation theory of groups

Cite

@article{arxiv.1105.2427,
  title  = {Small Galois groups that encode valuations},
  author = {Ido Efrat and Jan Minac},
  journal= {arXiv preprint arXiv:1105.2427},
  year   = {2011}
}

Comments

Final version. To appear in Acta Arithmetica

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