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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

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$57
Individual Members: US$34.20
Institutional Members: US$45.60
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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