**Contemporary Mathematics**

Volume: 155;
1994;
405 pp;
Softcover

MSC: Primary 00; 11; 14;

**Print ISBN: 978-0-8218-5154-8
Product Code: CONM/155**

List Price: $53.00

AMS Member Price: $42.40

MAA Member Price: $47.70

**Electronic ISBN: 978-0-8218-7746-3
Product Code: CONM/155.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

# Recent Advances in Real Algebraic Geometry and Quadratic Forms

Share this page *Edited by *
*William B. Jacob; Tsit-Yuen Lam; Robert O. Robson*

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

## Recent Advances in Real Algebraic Geometry and Quadratic Forms

- Contents v6 free
- Preface vii8 free
- D. W. Dubois and the Pioneer Days of Real Algebraic Geometry 110 free
- Papers on Real Algebraic Geometry 1120
- On Algebraic Structures of Manifolds 1120
- On Local Uniformization of Orderings 1928
- Real Algebraic Geometry Over p-Real Closed Fields 4756
- On the Reduction of Semialgebraic Sets by Real Valuations 7584
- Orderings for Noncommutative Rings 97106
- Nonexistence of Analytically Varying Solutions to Hilbert's 17th Problem 107116
- A Combinatorial Geometric Structure on the Space of Orders of a Field II 119128
- Formal Determination of Polynomial Consequences of Real Orthogonal Matrices 141150
- On Valuation Spectra 167176
- Minimal Generation of Basic Sets in the Real Spectrum of a Commutative Ring 207216
- A New Proof of the Homogeneous Nullstellensatz for p-Fields, and Applications to Topology 221230
- The Compatible Valuation Rings of the Coordinate Ring of the Real Plane 231240
- Estimates for Parametric Nonuniformity in Representations of a Definite Polynomial as a Sum of Fourth Powers 243252

- Papers on Quadratic Forms 247256
- On Generators for the Witt Ring 247256
- On the Trace Formula for Quadratic Forms 271280
- Quadratic Forms with Values in Line Bundles 293302
- On Annhilators in Graded Witt Rings and in Milnor's K-Theory 307316
- An Application of the Theory of Order Completions 321330
- Growth of the u-Invariant Under Algebraic Extensions 327336
- Remarks on Merkurjev's Investigations of the u-Invariant 333342
- On the Canonical Class of a Curve and the Extension Property for Quadratic Forms 339348
- Reduced Norms and Pfaflians Via Brauer-Severi Schemes 351360
- Matching Witts With Global Fields 365374
- On Witt-Kernels of Function Fields of Curves 389398
- On the Canonical Class of Hyperelliptic Curves 399408
- Epilogue 405414