BooksecrCollected Volumepp. 568–578

Detecting valuations using small Galois groups

  • Adam Topaz

    University of California, Berkeley, USA
Detecting valuations using small Galois groups cover

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Abstract

In this note we show how to detect valuations using almost-abelian pro- Galois groups of a field. In particular, we show that "commuting-liftable" subgroups of Galois groups arise, in a controlled way, from Kummer-duals of (principal-)units of valuations.