Valuation Theory and Its Applications

Valuation Theory and Its Applications

by Franz-Viktor Kuhlmann
     
 

ISBN-10: 0821832069

ISBN-13: 9780821832066

Pub. Date: 09/09/2003

Publisher: American Mathematical Society

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

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.

Product Details

ISBN-13:
9780821832066
Publisher:
American Mathematical Society
Publication date:
09/09/2003
Series:
Fields Institute Communications Series, #33
Pages:
459

Table of Contents

Prefaceix
Conference Detailsx
List of Participantsxi
Two Step Descent in Modular Galois Theory, Theorems of Burnside and Cayley, and Hilbert's Thirteenth Problem1
Generalized Taylor Formulae, Computations in Real Closed Valued Fields and Quantifier Elimination33
The Arithmetic-Arboreal Residue Structure of a Prufer Domain, I59
Left Valuation Rings, Left Cones, and a Question of Frege's81
Divisorial Valuations Dominating Rational Surface Singularities89
Valuations and Hermitian Forms on Skew Fields103
Resolution of Morphisms117
Rigid Subanalytic Sets141
Dubrovin Valuation Rings and Orders in Central Simple Algebras151
Q-adequate Bicyclic Bicubic Fields163
Valued Fields and Covers in Characteristic p175
Line Bundles on Rigid Analytic Spaces205
The Fixed-Point Theorems of Priess-Crampe and Ribenboim in Logic Programming219
The Minimum Property of Krasner's Constant237
About Merckel's Lemma247
Bounds for Representations of Polynomials Positive on Compact Semi-Algebraic Sets253
Model Theory of Real Closed Rings261
History of Valuation Theory-Part I291
A Density Property for PpC-fields357
Valuation Theory in Rigid Geometry and Curves over Valuation Rings369
Valuation Theory on Finite Dimensional Division Algebras385

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