Valuation theory and its applications
著者
書誌事項
Valuation theory and its applications
（Fields Institute communications, 32,
American Mathematical Society, c2002-2003
- v. 1
- v. 2
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注記
proceedings of the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan, Saskatoon, SK, Canada, 1999
Includes bibliographical references
内容説明・目次
- 巻冊次
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v. 1 ISBN 9780821828137
内容説明
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 Prufer 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.
目次
- Two step descent in modular Galois theory, theorems of Burnside and Cayley, and Hilbert's Thirteenth Problem
- Generalized Taylor formulae, computations in real closed valued fields and quantifier elimination
- The arithmetic-arboreal residue structure of a Prufer domain, I
- Left valuation rings, left cones, and a question of Frege's
- Divisorial valuations dominating rational surface singularities
- Valuations and Hermitian forms on skew fields
- Resolution of morphisms
- Rigid subanalytic sets
- Dubrovin valuation rings and orders in central simple algebras
- $Q$-adequate bicyclic bicubic fields
- Valued fields and covers in characteristic $p$, with an appendix by R. Guralnick
- Line bundles on rigid analytic spaces
- The fixed-point theorems of Priess-Crampe and Ribenboim in logic programming
- The minimum property of Krasner's constant
- About Merckel's lemma
- Bounds for representations of polynomials positive on compact semi-algebraic sets
- Model theory of real closed rings
- History of valuation theory-Part I
- A density property for PpC-fields
- Valuation theory in rigid geometry and curves over valuation rings
- Valuation theory on finite dimensional division algebras
- 巻冊次
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v. 2 ISBN 9780821832066
内容説明
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 Prufer 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. Also available from the AMS is ""Valuation Theory and Its Applications"", Volume I.
目次
A note on tame fields by K. Aghigh and S. K. Khanduja Some remarks about asymptotic couples by M. Aschenbrenner Prime segments for cones and rings by H. H. Brungs, H. Marubayashi, and E. Osmanagic Irreducibility criterion: A geometric point of view by V. Cossart and G. Moreno-Socias On the decidability of the existential theory of ${\mathbb F_p}[[t]]$ by J. Denef and H. Schoutens Galois groups over nonrigid fields by W. Gao, D. B. Leep, J. Minac, and T. L. Smith Automorphisms of formal power series rings over a valuation ring by B. Green Regular curves over Prufer domains by H. Knaf Encoding valuations in absolute Galois groups by J. Koenigsmann Dynamic computations inside the algebraic closure of a valued field by F.-V. Kuhlmann, H. Lombardi, and H. Perdry Preorders, rings, lattice-ordered groups and formal power series by G. Leloup The theorem of Grunwald-Wang in the setting of valuation theory by F. Lorenz and P. Roquette Invariants of singular plane curves by R. I. Michler $\mathcal V$-rational fields by J. Ohm A generalization of Hensel's lemma by H. Perdry Classically projective groups and pseudo classically closed fields by F. Pop Approximate roots by P. Popescu-Pampu Quantifier elimination for the relative Frobenius by T. Scanlon Ultrametric fixed point theorems and applications by E. Schorner Valuations, deformations, and toric geometry by B. Teissier.
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