Valuation Theory and Its Applications

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Overview

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 Prufer 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.

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Editorial Reviews

From The Critics
Valuation theory arose in the early 20th century in connection with number theory and has many important applications to geometry and analysis. In this proceedings volume, researchers from various branches of mathematics discuss recent developments in valuation theory. A sampling of topics includes rigid analytic geometry, real algebraic geometry, resolution of singularities, noncommutative valuation theory, and valuations on fields and Galois theory. This volume (one, the second is forthcoming) is not indexed. Annotation c. Book News, Inc., Portland, OR
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Product Details

Table of Contents

Preface
Ruth Ingrid Michler - In Memoriam
A Note on Tame Fields 1
Some Remarks About Asymptotic Couples 7
Prime Segments for Cones and Rings 19
Irreducibility Criterion: A Geometric Point of View 27
On the Decidability of the Existential Theory of F[subscript p][[t]] 43
Galois Groups Over Nonrigid Fields 61
Automorphisms of Formal Power Series Rings Over a Valuation Ring 79
Regular Curves Over Prufer Domains 89
Encoding Valuations in Absolute Galois Groups 107
Dynamic Computations Inside the Algebraic Closure of a Valued Field 133
Preorders, Rings, Lattice-ordered Groups and Formal Power Series 157
The Theorem of Grunwald-Wang in the Setting of Valuation Theory 175
Invariants of Singular Plane Curves 213
[nu]-rational Fields 229
A Generalization of Hensel's Lemma 241
Classically Projective Groups and Pseudo Classically Closed Fields 251
Approximate Roots 285
Quantifier Elimination for the Relative Frobenius 323
Ultrametric Fixed Point Theorems and Applications 353
Valuations, Deformations, and Toric Geometry 361
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