eBook ISBN:  9781470430665 
Product Code:  FIC/32.E 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 
eBook ISBN:  9781470430665 
Product Code:  FIC/32.E 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 

Book DetailsFields Institute CommunicationsVolume: 32; 2002; 449 ppMSC: Primary 12; Secondary 03; 11; 13; 14; 16; 20
This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada).
Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prüfer domains; the close connection to the famous resolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book is its focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory.
The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic. Also available from the AMS is Valuation Theory and Its Applications, Volume II.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.

Table of Contents

Chapters

Shreeram Abhyankar — Two step descent in modular Galois theory, theorems of Burnside and Cayley, and Hilbert’s Thirteenth Problem

MariEmi Alonso and Henri Lombardi — Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination

Şerban Basarab — The arithmeticarboreal residue structure of a Prüfer domain, I

HansHeinrich Brungs and Günter Törner — Left valuation rings, left cones, and a question of Frege’s

Vincent Cossart, Olivier Piltant and Ana RegueraLópez — Divisorial valuations dominating rational surface singularities

Thomas Craven — Valuations and Hermitian forms on skew fields

Steven Cutkosky — Resolution of morphisms

T. Gardener and Hans Schoutens — Rigid subanalytic sets

Joachim Gräter — Dubrovin valuation rings and orders in central simple algebras

Helen Grundman and Tara Smith — $Q$adequate bicyclic bicubic fields

David Harbater, Marius van der Put and Robert Guralnick — Valued fields and covers in characteristic $p$

Urs Hartl — Line bundles on rigid analytic spaces

Pascal Hitzler and Anthony Seda — The fixedpoint theorems of PriessCrampe and Ribenboim in logic programming

Sudesh Khanduja — The minimum property of Krasner’s constant

Henri Lombardi — About Merckel’s lemma

Alexander Prestel — Bounds for representations of polynomials positive on compact semialgebraic sets

Alexander Prestel and Niels Schwartz — Model theory of real closed rings

Peter Roquette — History of valuation theory—Part I

Joachim Schmid — A density property for PpCfields

Marius van der Put — Valuation theory in rigid geometry and curves over valuation rings

A. Wadsworth — Valuation theory on finite dimensional division algebras


Reviews

Altogether the two volumes give a vivid picture of the current state of the art in valuation theory and its applications.
CMS Notes


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This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada).
Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prüfer domains; the close connection to the famous resolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book is its focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory.
The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic. Also available from the AMS is Valuation Theory and Its Applications, Volume II.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.

Chapters

Shreeram Abhyankar — Two step descent in modular Galois theory, theorems of Burnside and Cayley, and Hilbert’s Thirteenth Problem

MariEmi Alonso and Henri Lombardi — Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination

Şerban Basarab — The arithmeticarboreal residue structure of a Prüfer domain, I

HansHeinrich Brungs and Günter Törner — Left valuation rings, left cones, and a question of Frege’s

Vincent Cossart, Olivier Piltant and Ana RegueraLópez — Divisorial valuations dominating rational surface singularities

Thomas Craven — Valuations and Hermitian forms on skew fields

Steven Cutkosky — Resolution of morphisms

T. Gardener and Hans Schoutens — Rigid subanalytic sets

Joachim Gräter — Dubrovin valuation rings and orders in central simple algebras

Helen Grundman and Tara Smith — $Q$adequate bicyclic bicubic fields

David Harbater, Marius van der Put and Robert Guralnick — Valued fields and covers in characteristic $p$

Urs Hartl — Line bundles on rigid analytic spaces

Pascal Hitzler and Anthony Seda — The fixedpoint theorems of PriessCrampe and Ribenboim in logic programming

Sudesh Khanduja — The minimum property of Krasner’s constant

Henri Lombardi — About Merckel’s lemma

Alexander Prestel — Bounds for representations of polynomials positive on compact semialgebraic sets

Alexander Prestel and Niels Schwartz — Model theory of real closed rings

Peter Roquette — History of valuation theory—Part I

Joachim Schmid — A density property for PpCfields

Marius van der Put — Valuation theory in rigid geometry and curves over valuation rings

A. Wadsworth — Valuation theory on finite dimensional division algebras

Altogether the two volumes give a vivid picture of the current state of the art in valuation theory and its applications.
CMS Notes