Recovering Higher Global and Local Fields from Galois Groups: An Algebraic Approach

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Abstract

A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an algebraic proof of the 0-dimensional case of Grothendieck's anabelian conjecture (proven by Pop), which says that finitely generated infinite fields are determined up to purely inseparable extensions by their absolute Galois groups. As a second application (which is a joint work with Fesenko) we analyze the arithmetic structure of fields with the same absolute Galois group as a higher-dimensional local field.
Original languageEnglish GB
Title of host publicationGeometry & Topology Monographs 3
PublisherMathematical Sciences Publishers
Pages273-279
Volume3
EditionPart II section 7
StatePublished - 2000

Publication series

NameGeometry & Topology Monographs
ISSN (Print)1464-8989
ISSN (Electronic)1464-8997

Keywords

  • math.NT
  • math.AG
  • 12E30, 12J25, 19M05

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