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Recent Advances in Real Algebraic Geometry and Quadratic Forms
Edited by: William B. Jacob, University of California, Santa Barbara, CA, Tsit-Yuen Lam, University of California, Berkeley, CA, and Robert O. Robson, Oregon State University, Corvallis, OR

Contemporary Mathematics
1994; 405 pp; softcover
Volume: 155
ISBN-10: 0-8218-5154-3
ISBN-13: 978-0-8218-5154-8
List Price: US$50
Member Price: US$40
Order Code: CONM/155
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The papers in this volume grew out of a year-long program in "Real Algebraic Geometry and Quadratic Forms", held at the University of California at Berkeley during the 1990-1991 academic year. This valuable collection of research articles by top workers serves as a record of current developments in these areas and as a tribute to the fruitful interaction between them. Students and researchers alike will find this book a useful reference, with articles ranging from the technical to the expository. Also included are summaries of the current developments in several sub-disciplines and indications of new research directions.


Graduate students and researchers in computational algebra and applications of real algebraic geometry.

Table of Contents

  • T. Recio and C. Andradas -- D. W. Dubois and the pioneer days of real algebraic geometry
  • Papers on real algebraic geometry
  • S. Akbulut -- On algebraic structures of manifolds
  • C. Andradas and J. M. Ruiz -- On local uniformization of orderings
  • R. Berr -- Real algebraic geometry over \(p\)-real closed fields
  • L. Bröcker -- On the reduction of semialgebraic sets by real valuations
  • T. C. Craven -- Orderings for noncommutative rings
  • C. N. Delzell -- Nonexistence of analytically varying solutions to Hilbert's 17th problem
  • M. A. Dickmann -- A combinatorial geometric structure on the space of orders of a field II
  • M. J. González-Lopez and T. Recio -- Formal determination of polynomial consequences of real orthogonal matrices
  • R. Huber and M. Knebusch -- On valuation spectra
  • M. Marshall -- Minimal generation of basic sets in the real spectrum of a commutative ring
  • A. Pfister -- A new proof of the homogeneous nullstellensatz for \(p\)-fields, and applications to topology
  • M. J. de la Puente -- The compatible valuation rings of the coordinate ring of the real plane
  • G. Stengle -- Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers
  • Papers on quadratic forms
  • J. Kr. Arason, R. Elman, and B. Jacob -- On generators for the Witt ring
  • E. Becker and T. Wöermann -- On the trace formula for quadratic forms
  • W. Bichsel and M.-A. Knus -- Quadratic forms with values in line bundles
  • M. Krüskemper -- On annihilators in graded Witt rings and in Milnor's \(K\)-theory
  • K. H. Leung -- An application of the theory of order completions
  • D. B. Leep and A. S. Merkurjev -- Growth of the \(u\)-invariant under algebraic extensions
  • J. Mináč -- Remarks on Merkurjev's investigations of the \(u\)-invariant
  • R. Parimala and W. Scharlau -- On the canonical class of a curve and the extension property for quadratic forms
  • R. Parimala and R. Sridharan -- Reduced norms and pfaffians via Brauer-Severi schemes
  • R. Perlis, K. Szymiczek, P. E. Conner, and R. Litherland -- Matching Witts with global fields
  • J. Shick -- On Witt-kernels of function fields of curves
  • V. Suresh -- On the canonical class of hyperelliptic curves
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