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Projective Group Structures as Absolute Galois Structures with Block Approximation
Dan Haran and Moshe Jarden, Tel Aviv University, Israel, and Florian Pop, University of Pennsylvania, Philadelphia, PA
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Memoirs of the American Mathematical Society
2007; 56 pp; softcover
Volume: 189
ISBN-10: 0-8218-3995-0
ISBN-13: 978-0-8218-3995-9
List Price: US$54
Individual Members: US$32.40
Institutional Members: US$43.20
Order Code: MEMO/189/884
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The authors prove: A proper profinite group structure \(\mathbf{G}\) is projective if and only if \(\mathbf{G}\) is the absolute Galois group structure of a proper field-valuation structure with block approximation.

Table of Contents

  • Introduction
  • Étale topology
  • Group structures
  • Completion of a cover to a cartesian square
  • Projective group structures
  • Special covers
  • Unirationally closed fields
  • Valued fields
  • The space of valuation of a field
  • Locally uniform \(v\)-adic topologies
  • Locally uniform Hensel's lemma
  • Field valuation structures
  • Block approximation
  • Rigid Henselian extensions
  • Projective group structures as absolute Galois structures
  • From field structures to field valuation structures
  • References
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