The Algebraic And Geometric Theory Of Quadratic Forms
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The Algebraic And Geometric Theory Of Quadratic Forms
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Author : Richard S. Elman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-07-15
The Algebraic And Geometric Theory Of Quadratic Forms written by Richard S. Elman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-15 with Mathematics categories.
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.
Quadratic Forms Algebra Arithmetic And Geometry
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Author : Ricardo Baeza
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-08-14
Quadratic Forms Algebra Arithmetic And Geometry written by Ricardo Baeza and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-14 with Mathematics categories.
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.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author : Oleg T. Izhboldin
language : en
Publisher: Springer
Release Date : 2004-02-07
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by Oleg T. Izhboldin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-07 with Mathematics categories.
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.
Bilinear Algebra
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Author : Kazimierz Szymiczek
language : en
Publisher: Routledge
Release Date : 2017-11-22
Bilinear Algebra written by Kazimierz Szymiczek and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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 Theory Of Quadratic Forms
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Author : Tsit-Yuen Lam
language : en
Publisher:
Release Date : 1973
The Algebraic Theory Of Quadratic Forms written by Tsit-Yuen Lam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algebraic fields categories.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author : Oleg T Tignol Jean-Pierre Izhboldin
language : en
Publisher: Springer
Release Date : 2014-01-15
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by Oleg T Tignol Jean-Pierre Izhboldin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Algebraic Theory Of Quadratic Forms
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Author : Manfred Knebusch
language : en
Publisher: Birkhäuser
Release Date : 1980
Algebraic Theory Of Quadratic Forms written by Manfred Knebusch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Juvenile Nonfiction categories.
Recent Advances In Real Algebraic Geometry And Quadratic Forms
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Author : Bill Jacob
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Recent Advances In Real Algebraic Geometry And Quadratic Forms written by Bill Jacob and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The papers collected here present an up-to-date record of the current research developments in the fields of real algebraic geometry and quadratic forms. Articles range from the technical to the expository and there are also indications to new research directions.
Introduction To Quadratic Forms Over Fields
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Author : Tsit-Yuen Lam
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Introduction To Quadratic Forms Over Fields written by Tsit-Yuen Lam and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Forms, Quadratic categories.
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.
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author :
language : en
Publisher:
Release Date : 2004
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algebraic fields categories.