Commuting-Liftable Subgroups of Galois Groups II

Abstract

Let $n$ denote either a positive integer or $\infty$, let $\ell$ be a fixed prime and let $K$ be a field of characteristic different from $\ell$. In the presence of sufficiently many roots of unity in $K$, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal ${\ell }^n$-abelian Galois group of $K$ using the maximal ${\ell }^N$-abelian-by-central Galois group of $K$, whenever $N$ is sufficiently large relative to $n$.

62 pages; final version; NOTE: numbering has changed from previous versions

References in corpus (2)

• Almost-Commuting-Liftable Subgroups of Galois Groups
• Small Galois groups that encode valuations

Cited by in corpus (7)

• Galois groups and cohomological functors
• A Torelli Theorem for Higher-Dimensional Function Fields
• Reconstructing function fields from rational quotients of mod-$\ell$ Galois groups
• Reconstruction of Function Fields from their pro-l abelian divisorial Inertia
• Recovering function fields from their integral $\ell$-adic cohomology with the Galois action
• The Galois action on geometric lattices and the mod-$\ell$ I/OM
• Characterising local fields of positive characteristic by Galois theory and the Brauer group