Memoirs of the American Mathematical Society 2007; 56 pp; softcover Volume: 189 ISBN10: 0821839950 ISBN13: 9780821839959 List Price: US$57 Individual Members: US$34.20 Institutional Members: US$45.60 Order Code: MEMO/189/884
 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 fieldvaluation 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
