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Bilinear Algebra

2017-11-22 Mathematics
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Release : 2017-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 205/5 ( reviews)

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Book Synopsis Bilinear Algebra by : Kazimierz Szymiczek

Download or read book Bilinear Algebra written by Kazimierz Szymiczek. This book was released on 2017-11-22. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.

The Algebraic and Geometric Theory of Quadratic Forms

2008-07-15 Mathematics
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Release : 2008-07-15
Genre : Mathematics
Kind : eBook
Book Rating : 229/5 ( reviews)

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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. This book was released on 2008-07-15. 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.

The Algebraic Theory of Quadratic Forms

1973 Algebraic fields
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Release : 1973
Genre : Algebraic fields
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis The Algebraic Theory of Quadratic Forms by : Tsit-Yuen Lam

Download or read book The Algebraic Theory of Quadratic Forms written by Tsit-Yuen Lam. This book was released on 1973. Available in PDF, EPUB and Kindle. Book excerpt:

Bilinear Algebra

2017-11-22 Mathematics
Download Bilinear Algebra PDF Online Free

Author :
Release : 2017-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 213/5 ( reviews)

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Book Synopsis Bilinear Algebra by : Kazimierz Szymiczek

Download or read book Bilinear Algebra written by Kazimierz Szymiczek. This book was released on 2017-11-22. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.

Geometric Methods in the Algebraic Theory of Quadratic Forms

2004-02-07 Mathematics
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Release : 2004-02-07
Genre : Mathematics
Kind : eBook
Book Rating : 904/5 ( reviews)

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Book Synopsis Geometric Methods in the Algebraic Theory of Quadratic Forms by : Oleg T. Izhboldin

Download or read book Geometric Methods in the Algebraic Theory of Quadratic Forms written by Oleg T. Izhboldin. This book was released on 2004-02-07. Available in PDF, EPUB and Kindle. Book excerpt: The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

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