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Softcover ISBN:  9780821851548 
Product Code:  CONM/155 
List Price:  $130.00 
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Book DetailsContemporary MathematicsVolume: 155; 1994; 405 ppMSC: Primary 00; 11; 14
The papers in this volume grew out of a yearlong 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 subdisciplines and indications of new research directions.
ReadershipGraduate students and researchers in computational algebra and applications of real algebraic geometry.

Table of Contents

Articles

Tomás Recio and Carlos Andradas — D. W. Dubois and the pioneer days of real algebraic geometry [ MR 1260698 ]

S. Akbulut — On algebraic structures of manifolds [ MR 1260699 ]

Carlos Andradas and Jesús M. Ruiz — On local uniformization of orderings [ MR 1260700 ]

Ralph Berr — Real algebraic geometry over $p$real closed fields [ MR 1260701 ]

Ludwig Bröcker — On the reduction of semialgebraic sets by real valuations [ MR 1260702 ]

Thomas C. Craven — Orderings for noncommutative rings [ MR 1260703 ]

Charles N. Delzell — Nonexistence of analytically varying solutions to Hilbert’s 17th problem [ MR 1260704 ]

M. A. Dickmann — A combinatorial geometric structure on the space of orders of a field. II [ MR 1260705 ]

M. J. GonzálezLópez and T. Recio — Formal determination of polynomial consequences of real orthogonal matrices [ MR 1260706 ]

Roland Huber and Manfred Knebusch — On valuation spectra [ MR 1260707 ]

M. Marshall — Minimal generation of basic sets in the real spectrum of a commutative ring [ MR 1260708 ]

Albrecht Pfister — A new proof of the homogeneous Nullstellensatz for $p$fields, and applications to topology [ MR 1260709 ]

M. J. de la Puente — The compatible valuation rings of the coordinate ring of the real plane [ MR 1260710 ]

Gilbert Stengle — Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers [ MR 1260711 ]

Jón Kr. Arason, Richard Elman and Bill Jacob — On generators for the Witt ring [ MR 1260712 ]

Eberhard Becker and Thorsten Wöermann — On the trace formula for quadratic forms [ MR 1260713 ]

W. Bichsel and M.A. Knus — Quadratic forms with values in line bundles [ MR 1260714 ]

Martin Krüskemper — On annihilators in graded Witt rings and in Milnor’s $K$theory [ MR 1260715 ]

Ka Hin Leung — An application of the theory of order completions [ MR 1260716 ]

David B. Leep and A. S. Merkurjev — Growth of the $u$invariant under algebraic extensions [ MR 1260717 ]

Ján Mináč — Remarks on Merkurjev’s investigations of the $u$invariant [ MR 1260718 ]

R. Parimala and W. Scharlau — On the canonical class of a curve and the extension property for quadratic forms [ MR 1260719 ]

R. Parimala and R. Sridharan — Reduced norms and Pfaffians via BrauerSeveri schemes [ MR 1260720 ]

R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland — Matching Witts with global fields [ MR 1260721 ]

Jonathan Shick — On Wittkernels of function fields of curves [ MR 1260722 ]

V. Suresh — On the canonical class of hyperelliptic curves [ MR 1260723 ]


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The papers in this volume grew out of a yearlong 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 subdisciplines and indications of new research directions.
Graduate students and researchers in computational algebra and applications of real algebraic geometry.

Articles

Tomás Recio and Carlos Andradas — D. W. Dubois and the pioneer days of real algebraic geometry [ MR 1260698 ]

S. Akbulut — On algebraic structures of manifolds [ MR 1260699 ]

Carlos Andradas and Jesús M. Ruiz — On local uniformization of orderings [ MR 1260700 ]

Ralph Berr — Real algebraic geometry over $p$real closed fields [ MR 1260701 ]

Ludwig Bröcker — On the reduction of semialgebraic sets by real valuations [ MR 1260702 ]

Thomas C. Craven — Orderings for noncommutative rings [ MR 1260703 ]

Charles N. Delzell — Nonexistence of analytically varying solutions to Hilbert’s 17th problem [ MR 1260704 ]

M. A. Dickmann — A combinatorial geometric structure on the space of orders of a field. II [ MR 1260705 ]

M. J. GonzálezLópez and T. Recio — Formal determination of polynomial consequences of real orthogonal matrices [ MR 1260706 ]

Roland Huber and Manfred Knebusch — On valuation spectra [ MR 1260707 ]

M. Marshall — Minimal generation of basic sets in the real spectrum of a commutative ring [ MR 1260708 ]

Albrecht Pfister — A new proof of the homogeneous Nullstellensatz for $p$fields, and applications to topology [ MR 1260709 ]

M. J. de la Puente — The compatible valuation rings of the coordinate ring of the real plane [ MR 1260710 ]

Gilbert Stengle — Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers [ MR 1260711 ]

Jón Kr. Arason, Richard Elman and Bill Jacob — On generators for the Witt ring [ MR 1260712 ]

Eberhard Becker and Thorsten Wöermann — On the trace formula for quadratic forms [ MR 1260713 ]

W. Bichsel and M.A. Knus — Quadratic forms with values in line bundles [ MR 1260714 ]

Martin Krüskemper — On annihilators in graded Witt rings and in Milnor’s $K$theory [ MR 1260715 ]

Ka Hin Leung — An application of the theory of order completions [ MR 1260716 ]

David B. Leep and A. S. Merkurjev — Growth of the $u$invariant under algebraic extensions [ MR 1260717 ]

Ján Mináč — Remarks on Merkurjev’s investigations of the $u$invariant [ MR 1260718 ]

R. Parimala and W. Scharlau — On the canonical class of a curve and the extension property for quadratic forms [ MR 1260719 ]

R. Parimala and R. Sridharan — Reduced norms and Pfaffians via BrauerSeveri schemes [ MR 1260720 ]

R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland — Matching Witts with global fields [ MR 1260721 ]

Jonathan Shick — On Wittkernels of function fields of curves [ MR 1260722 ]

V. Suresh — On the canonical class of hyperelliptic curves [ MR 1260723 ]