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Hardcover ISBN:  9780821832066 
Product Code:  FIC/33 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
eBook ISBN:  9781470430672 
Product Code:  FIC/33.E 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 
Hardcover ISBN:  9780821832066 
eBook ISBN:  9781470430672 
Product Code:  FIC/33.B 
List Price:  $300.00 $227.50 
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AMS Member Price:  $240.00 $182.00 

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.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
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.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
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