Abelian-by-Central Galois Groups of Fields II: Definability of Inertia/Decomposition Groups
Abstract
This paper explores some first-order properties of commuting-liftable pairs in pro- abelian-by-central Galois groups of fields. The main focus of the paper is to prove that minimized inertia and decomposition groups of many valuations are first-order definable using a predicate for the collection of commuting-liftable pairs.
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