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Valuation Theory and Its Applications, Volume II
Edited by: Franz-Viktor Kuhlmann, Salma Kuhlmann, and Murray Marshall, University of Saskatchewan, Saskatoon, SK, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
2003; 459 pp; hardcover
Volume: 33
ISBN-10: 0-8218-3206-9
ISBN-13: 978-0-8218-3206-6
List Price: US$138
Member Price: US$110.40
Order Code: FIC/33
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This book is the second of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). It contains the most recent applications of valuation theory to a broad range of mathematical ideas. Valuation theory arose in the early part of the twentieth century in connection with number theory and continues to have many important applications to algebra, geometry, and analysis.

The research and survey papers in this volume cover a variety of topics, including Galois theory, the Grunwald-Wang Theorem, algebraic geometry, resolution of singularities, curves over Prüfer domains, model theory of valued fields and the Frobenius, Hardy fields, Hensel's Lemma, fixed point theorems, and computations in valued fields.

It is suitable for graduate students and research mathematicians interested in algebra, algebraic geometry, number theory, and mathematical logic.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Graduate students and research mathematicians interested in algebra, algebraic geometry, number theory, and mathematical logic.

Table of Contents

  • K. Aghigh and S. K. Khanduja -- A note on tame fields
  • M. Aschenbrenner -- Some remarks about asymptotic couples
  • H. H. Brungs, H. Marubayashi, and E. Osmanagic -- Prime segments for cones and rings
  • V. Cossart and G. Moreno-Socías -- Irreducibility criterion: A geometric point of view
  • J. Denef and H. Schoutens -- On the decidability of the existential theory of \({\mathbb F_p}[[t]]\)
  • W. Gao, D. B. Leep, J. Mináč, and T. L. Smith -- Galois groups over nonrigid fields
  • B. Green -- Automorphisms of formal power series rings over a valuation ring
  • H. Knaf -- Regular curves over Prüfer domains
  • J. Koenigsmann -- Encoding valuations in absolute Galois groups
  • F.-V. Kuhlmann, H. Lombardi, and H. Perdry -- Dynamic computations inside the algebraic closure of a valued field
  • G. Leloup -- Preorders, rings, lattice-ordered groups and formal power series
  • F. Lorenz and P. Roquette -- The theorem of Grunwald-Wang in the setting of valuation theory
  • R. I. Michler -- Invariants of singular plane curves
  • J. Ohm -- \(\mathcal V\)-rational fields
  • H. Perdry -- A generalization of Hensel's lemma
  • F. Pop -- Classically projective groups and pseudo classically closed fields
  • P. Popescu-Pampu -- Approximate roots
  • T. Scanlon -- Quantifier elimination for the relative Frobenius
  • E. Schörner -- Ultrametric fixed point theorems and applications
  • B. Teissier -- Valuations, deformations, and toric geometry
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