Abelian-by-Central Galois Groups of Fields II: Definability of Inertia/Decomposition Groups

2015/03/15 by Topaz, Adam
#12E30 #12F10 #12J20 #20E18 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1503.04368

Abstract

This paper explores some first-order properties of commuting-liftable pairs in pro-ℓ 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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