Small Galois groups that encode valuations

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.

Final version. To appear in Acta Arithmetica

References in corpus (2)

• Introduction to birational anabelian geometry
• Galois groups and cohomological functors

Cited by in corpus (1)

• Commuting-Liftable Subgroups of Galois Groups II