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Abelian-by-central Galois groups of fields II: Definability of inertia/decomposition groups

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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. For higher-dimensional function fields over algebraically closed fields, we show that the minimized inertia and decomposition groups of quasi-divisorial valuations are uniformly first-order definable in this language.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley 970 Evans Hall #3840, Berkeley, CA., 94720-384, USA

    Adam Topaz

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  1. Adam Topaz
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Correspondence to Adam Topaz.

Additional information

This research was supported by NSF postdoctoral fellowship DMS-1304114.

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Topaz, A. Abelian-by-central Galois groups of fields II: Definability of inertia/decomposition groups. Isr. J. Math. 215, 713–748 (2016). https://doi.org/10.1007/s11856-016-1392-8

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  • DOI: https://doi.org/10.1007/s11856-016-1392-8

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