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Valuation Theory and Its Applications, Volume I
 
Edited by: Franz-Viktor Kuhlmann University of Saskatchewan, Saskatoon, SK, Canada
Salma Kuhlmann University of Saskatchewan, Saskatoon, SK, Canada
Murray Marshall University of Saskatchewan, Saskatoon, SK, Canada
A co-publication of the AMS and Fields Institute
Valuation Theory and Its Applications, Volume I
eBook ISBN:  978-1-4704-3066-5
Product Code:  FIC/32.E
List Price: $145.00
MAA Member Price: $130.50
AMS Member Price: $116.00
Valuation Theory and Its Applications, Volume I
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Valuation Theory and Its Applications, Volume I
Edited by: Franz-Viktor Kuhlmann University of Saskatchewan, Saskatoon, SK, Canada
Salma Kuhlmann University of Saskatchewan, Saskatoon, SK, Canada
Murray Marshall University of Saskatchewan, Saskatoon, SK, Canada
A co-publication of the AMS and Fields Institute
eBook ISBN:  978-1-4704-3066-5
Product Code:  FIC/32.E
List Price: $145.00
MAA Member Price: $130.50
AMS Member Price: $116.00
  • Book Details
     
     
    Fields Institute Communications
    Volume: 322002; 449 pp
    MSC: 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 co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

    Readership

    Graduate 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
    • Mari-Emi Alonso and Henri Lombardi — Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination
    • Şerban Basarab — The arithmetic-arboreal residue structure of a Prüfer domain, I
    • Hans-Heinrich Brungs and Günter Törner — Left valuation rings, left cones, and a question of Frege’s
    • Vincent Cossart, Olivier Piltant and Ana Reguera-López — 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 fixed-point theorems of Priess-Crampe 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 semi-algebraic 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 PpC-fields
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 322002; 449 pp
MSC: 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 co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

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
  • Mari-Emi Alonso and Henri Lombardi — Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination
  • Şerban Basarab — The arithmetic-arboreal residue structure of a Prüfer domain, I
  • Hans-Heinrich Brungs and Günter Törner — Left valuation rings, left cones, and a question of Frege’s
  • Vincent Cossart, Olivier Piltant and Ana Reguera-López — 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 fixed-point theorems of Priess-Crampe 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 semi-algebraic 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 PpC-fields
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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