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.

Readership

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