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Recent Advances in Real Algebraic Geometry and Quadratic Forms
 
Edited by: William B. Jacob University of California, Santa Barbara, Santa Barbara, CA
Tsit-Yuen Lam University of California, Berkeley, Berkeley, CA
Robert O. Robson University of Oregon, Corvallis, OR
Recent Advances in Real Algebraic Geometry and Quadratic Forms
Softcover ISBN:  978-0-8218-5154-8
Product Code:  CONM/155
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7746-3
Product Code:  CONM/155.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-5154-8
eBook: ISBN:  978-0-8218-7746-3
Product Code:  CONM/155.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Recent Advances in Real Algebraic Geometry and Quadratic Forms
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Recent Advances in Real Algebraic Geometry and Quadratic Forms
Edited by: William B. Jacob University of California, Santa Barbara, Santa Barbara, CA
Tsit-Yuen Lam University of California, Berkeley, Berkeley, CA
Robert O. Robson University of Oregon, Corvallis, OR
Softcover ISBN:  978-0-8218-5154-8
Product Code:  CONM/155
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7746-3
Product Code:  CONM/155.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-5154-8
eBook ISBN:  978-0-8218-7746-3
Product Code:  CONM/155.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1551994; 405 pp
    MSC: Primary 00; 11; 14;

    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
     
     
    • 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. González-López 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 Brauer-Severi schemes [ MR 1260720 ]
    • R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland — Matching Witts with global fields [ MR 1260721 ]
    • Jonathan Shick — On Witt-kernels of function fields of curves [ MR 1260722 ]
    • V. Suresh — On the canonical class of hyperelliptic curves [ MR 1260723 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1551994; 405 pp
MSC: Primary 00; 11; 14;

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.

  • 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. González-López 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 Brauer-Severi schemes [ MR 1260720 ]
  • R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland — Matching Witts with global fields [ MR 1260721 ]
  • Jonathan Shick — On Witt-kernels of function fields of curves [ MR 1260722 ]
  • V. Suresh — On the canonical class of hyperelliptic curves [ MR 1260723 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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