Small Galois groups that encode valuations

Ido Efrat; Jan Minac

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arXiv · 1105.2427

Small Galois groups that encode valuations

Ido Efrat·Jan Minac

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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.

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Ido Efrat, Jan Minac. 2011-05-12. Small Galois groups that encode valuations. https://arxiv.org/abs/1105.2427

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