Fields Institute Communications 2003; 459 pp; hardcover Volume: 33 ISBN10: 0821832069 ISBN13: 9780821832066 List Price: US$131 Member Price: US$104.80 Order Code: FIC/33
 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 GrunwaldWang 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 copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership 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. MorenoSocías  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, latticeordered groups and formal power series
 F. Lorenz and P. Roquette  The theorem of GrunwaldWang 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. PopescuPampu  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
