**Fields Institute Communications**

Volume: 33;
2003;
459 pp;
Hardcover

MSC: Primary 12;
Secondary 03; 11; 13; 14; 16; 20

**Print ISBN: 978-0-8218-3206-6
Product Code: FIC/33**

List Price: $147.00

AMS Member Price: $117.60

MAA Member Price: $132.30

**Electronic ISBN: 978-1-4704-3067-2
Product Code: FIC/33.E**

List Price: $138.00

AMS Member Price: $110.40

MAA Member Price: $124.20

# Valuation Theory and Its Applications, Volume II

Share this page *Edited by *
*Franz-Viktor Kuhlmann; Salma Kuhlmann; Murray Marshall*

A co-publication of the AMS and Fields Institute

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 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 co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

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

# Table of Contents

## Valuation Theory and Its Applications, Volume II

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- In memoriam xi12
- A note on tame fields 114
- Some remarks about asymptotic couples 720
- Prime segments for cones and rings 1932
- Irreducibility criterion: A geometric point of view 2740
- On the decidability of the existential theory of 𝔽_{𝕡}[[𝕥]] 4356
- Galois groups over nonrigid fields 6174
- Automorphisms of formal power series rings over a valuation ring 7992
- Regular curves over Prüfer domains 89102
- Encoding valuations in absolute Galois groups 107120
- Dynamic computations inside the algebraic closure of a valued field 133146
- Preorders, rings, lattice-ordered groups and formal power series 157170
- The theorem of Grunwald-Wang in the setting of valuation theory 175188
- Invariants of singular plane curves 213226
- 𝒱-rational fields 229242
- A generalization of Hensel’s lemma 241254
- Classically projective groups and pseudo classically closed fields 251264
- Approximate roots 285298
- Quantifier elimination for the relative Frobenius 323336
- Ultrametric fixed point theorems and applications 353366
- Valuations, deformations, and toric geometry 361374
- Back Cover Back Cover1473