Hardcover ISBN:  9780821832066 
Product Code:  FIC/33 
List Price:  $147.00 
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AMS Member Price:  $117.60 
Electronic ISBN:  9781470430672 
Product Code:  FIC/33.E 
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Book DetailsFields Institute CommunicationsVolume: 33; 2003; 459 ppMSC: Primary 12; Secondary 03; 11; 13; 14; 16; 20;
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.ReadershipGraduate students and research mathematicians interested in algebra, algebraic geometry, number theory, and mathematical logic.

Table of Contents

Chapters

Kamal Aghigh and Sudesh Khanduja  A note on tame fields

Matthias Aschenbrenner  Some remarks about asymptotic couples

H. Brungs, H. Marubayashi and E. Osmanagic  Prime segments for cones and rings

Vincent Cossart and Guillermo MorenoSocías  Irreducibility criterion: A geometric point of view

Jan Denef and Hans Schoutens  On the decidability of the existential theory of ${\mathbb F_p}[[t]]$

Wenfeng Gao, David Leep, Ján Mináč and Tara Smith  Galois groups over nonrigid fields

Barry Green  Automorphisms of formal power series rings over a valuation ring

Hagen Knaf  Regular curves over Prüfer domains

Jochen Koenigsmann  Encoding valuations in absolute Galois groups

FranzViktor Kuhlmann, Henri Lombardi and Hervé Perdry  Dynamic computations inside the algebraic closure of a valued field

Gérard Leloup  Preorders, rings, latticeordered groups and formal power series

Falko Lorenz and Peter Roquette  The theorem of GrunwaldWang in the setting of valuation theory

Ruth Michler  Invariants of singular plane curves

Jack Ohm  $\mathcal V$rational fields

Hervé Perdry  A generalization of Hensel’s lemma

Florian Pop  Classically projective groups and pseudo classically closed fields

Patrick PopescuPampu  Approximate roots

Thomas Scanlon  Quantifier elimination for the relative Frobenius

Erwin Schörner  Ultrametric fixed point theorems and applications

Bernard Teissier  Valuations, deformations, and toric geometry


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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.
Graduate students and research mathematicians interested in algebra, algebraic geometry, number theory, and mathematical logic.

Chapters

Kamal Aghigh and Sudesh Khanduja  A note on tame fields

Matthias Aschenbrenner  Some remarks about asymptotic couples

H. Brungs, H. Marubayashi and E. Osmanagic  Prime segments for cones and rings

Vincent Cossart and Guillermo MorenoSocías  Irreducibility criterion: A geometric point of view

Jan Denef and Hans Schoutens  On the decidability of the existential theory of ${\mathbb F_p}[[t]]$

Wenfeng Gao, David Leep, Ján Mináč and Tara Smith  Galois groups over nonrigid fields

Barry Green  Automorphisms of formal power series rings over a valuation ring

Hagen Knaf  Regular curves over Prüfer domains

Jochen Koenigsmann  Encoding valuations in absolute Galois groups

FranzViktor Kuhlmann, Henri Lombardi and Hervé Perdry  Dynamic computations inside the algebraic closure of a valued field

Gérard Leloup  Preorders, rings, latticeordered groups and formal power series

Falko Lorenz and Peter Roquette  The theorem of GrunwaldWang in the setting of valuation theory

Ruth Michler  Invariants of singular plane curves

Jack Ohm  $\mathcal V$rational fields

Hervé Perdry  A generalization of Hensel’s lemma

Florian Pop  Classically projective groups and pseudo classically closed fields

Patrick PopescuPampu  Approximate roots

Thomas Scanlon  Quantifier elimination for the relative Frobenius

Erwin Schörner  Ultrametric fixed point theorems and applications

Bernard Teissier  Valuations, deformations, and toric geometry