Specialization of Quadratic and Symmetric Bilinear Forms

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Publisher : Springer Science & Business Media
ISBN 13 : 1848822421
Total Pages : 202 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Specialization of Quadratic and Symmetric Bilinear Forms by : Manfred Knebusch

Download or read book Specialization of Quadratic and Symmetric Bilinear Forms written by Manfred Knebusch and published by Springer Science & Business Media. This book was released on 2011-01-22 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematician Said Who Can Quote Me a Theorem that’s True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It is—poetic exaggeration allowed—a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has “good reduction” with respect to? (see§1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of?. The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of Izhboldin–Kahn–Karpenko–Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there).

Quadratic Forms -- Algebra, Arithmetic, and Geometry

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821846485
Total Pages : 424 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quadratic Forms -- Algebra, Arithmetic, and Geometry by : Ricardo Baeza

Download or read book Quadratic Forms -- Algebra, Arithmetic, and Geometry written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2009-08-14 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.

Orderings, Valuations and Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 0821807021
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orderings, Valuations and Quadratic Forms by : Tsit-Yuen Lam

Download or read book Orderings, Valuations and Quadratic Forms written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 1983 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to ordered fields and reduced quadratic forms using valuation-theoretic techniques. This book describes the techniques of residue forms and the relevant Springer theory.

Introduction to Quadratic Forms over Fields

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Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Quadratic Forms over Fields by : Tsit-Yuen Lam

Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.

Quadratic and Hermitian Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821860083
Total Pages : 362 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Quadratic and Hermitian Forms by : McMaster University

Download or read book Quadratic and Hermitian Forms written by McMaster University and published by American Mathematical Soc.. This book was released on 1984 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).

Quadratic Mappings and Clifford Algebras

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Publisher : Springer Science & Business Media
ISBN 13 : 3764386061
Total Pages : 512 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quadratic Mappings and Clifford Algebras by : Jacques Helmstetter

Download or read book Quadratic Mappings and Clifford Algebras written by Jacques Helmstetter and published by Springer Science & Business Media. This book was released on 2008-05-24 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods.

The Algebraic and Geometric Theory of Quadratic Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821873229
Total Pages : 456 pages
Book Rating : 4.8/5 (732 download)

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Book Synopsis The Algebraic and Geometric Theory of Quadratic Forms by : Richard S. Elman

Download or read book The Algebraic and Geometric Theory of Quadratic Forms written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 2008-07-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

Algebraic and Arithmetic Theory of Quadratic Forms

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 082183441X
Total Pages : 364 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Arithmetic Theory of Quadratic Forms by : Ricardo Baeza

Download or read book Algebraic and Arithmetic Theory of Quadratic Forms written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2004 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.

Geometrie algebrique reelle et formes quadratiques

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Publisher : Springer
ISBN 13 : 3540395482
Total Pages : 471 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Geometrie algebrique reelle et formes quadratiques by : J.-L. Colliot-Thelene

Download or read book Geometrie algebrique reelle et formes quadratiques written by J.-L. Colliot-Thelene and published by Springer. This book was released on 2006-11-15 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic K — Theory

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Publisher : Springer
ISBN 13 : 3540395563
Total Pages : 421 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Algebraic K — Theory by : R. Keith Dennis

Download or read book Algebraic K — Theory written by R. Keith Dennis and published by Springer. This book was released on 2006-11-15 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Methods in Commutative Algebra

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Publisher : CRC Press
ISBN 13 : 9780824712822
Total Pages : 308 pages
Book Rating : 4.7/5 (128 download)

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Book Synopsis Analytic Methods in Commutative Algebra by : Richard N. Draper

Download or read book Analytic Methods in Commutative Algebra written by Richard N. Draper and published by CRC Press. This book was released on 1982-04-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Acta arithmetica

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Publisher :
ISBN 13 :
Total Pages : 576 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis Acta arithmetica by :

Download or read book Acta arithmetica written by and published by . This book was released on 1973 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Theory of Quadratic Forms

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Publisher : Birkhäuser
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (43 download)

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Book Synopsis Algebraic Theory of Quadratic Forms by : Manfred Knebusch

Download or read book Algebraic Theory of Quadratic Forms written by Manfred Knebusch and published by Birkhäuser. This book was released on 1980 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conference on Quadratic Forms, 1976

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Publisher : Kingston, Ont. : Queen's University
ISBN 13 :
Total Pages : 716 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Conference on Quadratic Forms, 1976 by : G. Orzech

Download or read book Conference on Quadratic Forms, 1976 written by G. Orzech and published by Kingston, Ont. : Queen's University. This book was released on 1977 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ten Lectures on Quadratic Forms Over Fields

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Publisher :
ISBN 13 :
Total Pages : 726 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Ten Lectures on Quadratic Forms Over Fields by : G. Orzech

Download or read book Ten Lectures on Quadratic Forms Over Fields written by G. Orzech and published by . This book was released on 1977 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt:

$K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 0821803409
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras by : Bill Jacob

Download or read book $K$-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of two - also available in a set of both volumes.

Reviews in Number Theory 1973-83

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Publisher :
ISBN 13 :
Total Pages : 844 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Reviews in Number Theory 1973-83 by : Richard K. Guy

Download or read book Reviews in Number Theory 1973-83 written by Richard K. Guy and published by . This book was released on 1984 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: