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.
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Für höhere Schule und Studium
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ISBN-13
978-0-8218-2813-7 (9780821828137)
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Schweitzer Klassifikation
Herausgeber*in
all of the University of Saskatchewan, Saskatoon, Canada
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
