Author: Richard S. Elman
Publisher: American Mathematical Soc.
ISBN: 9780821873229
Category : Mathematics
Languages : en
Pages : 456
Book Description
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 and Geometric Theory of Quadratic Forms
Author: Richard S. Elman
Publisher: American Mathematical Soc.
ISBN: 9780821873229
Category : Mathematics
Languages : en
Pages : 456
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 9780821873229
Category : Mathematics
Languages : en
Pages : 456
Book Description
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.
Geometric Methods in the Algebraic Theory of Quadratic Forms
Author:
Publisher: Springer Science & Business Media
ISBN: 9783540207283
Category : Forms, Pfister
Languages : en
Pages : 212
Book Description
Publisher: Springer Science & Business Media
ISBN: 9783540207283
Category : Forms, Pfister
Languages : en
Pages : 212
Book Description
Quadratic Forms -- Algebra, Arithmetic, and Geometry
Author: Ricardo Baeza
Publisher: American Mathematical Soc.
ISBN: 0821846485
Category : Mathematics
Languages : en
Pages : 424
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821846485
Category : Mathematics
Languages : en
Pages : 424
Book Description
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.
Quadratic Forms with Applications to Algebraic Geometry and Topology
Author: Albrecht Pfister
Publisher: Cambridge University Press
ISBN: 0521467551
Category : Mathematics
Languages : en
Pages : 191
Book Description
A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Publisher: Cambridge University Press
ISBN: 0521467551
Category : Mathematics
Languages : en
Pages : 191
Book Description
A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Recent Advances in Real Algebraic Geometry and Quadratic Forms
Author: Bill Jacob
Publisher: American Mathematical Soc.
ISBN: 0821851543
Category : Mathematics
Languages : en
Pages : 405
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821851543
Category : Mathematics
Languages : en
Pages : 405
Book Description
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.
Bilinear Algebra
Author: Kazimierz Szymiczek
Publisher: Routledge
ISBN: 1351464213
Category : Mathematics
Languages : en
Pages : 496
Book Description
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.
Publisher: Routledge
ISBN: 1351464213
Category : Mathematics
Languages : en
Pages : 496
Book Description
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
Author: Oleg T Tignol Jean-Pierre Izhboldin
Publisher: Springer
ISBN: 9783662177747
Category :
Languages : en
Pages : 212
Book Description
Publisher: Springer
ISBN: 9783662177747
Category :
Languages : en
Pages : 212
Book Description
Quadratic Forms, Linear Algebraic Groups, and Cohomology
Author: Skip Garibaldi
Publisher: Springer Science & Business Media
ISBN: 1441962115
Category : Mathematics
Languages : en
Pages : 348
Book Description
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.
Publisher: Springer Science & Business Media
ISBN: 1441962115
Category : Mathematics
Languages : en
Pages : 348
Book Description
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.
The Algebraic Theory of Quadratic Forms
Author: Tsit-Yuen Lam
Publisher: Addison-Wesley
ISBN: 9780805356663
Category : Mathematics
Languages : en
Pages : 344
Book Description
Publisher: Addison-Wesley
ISBN: 9780805356663
Category : Mathematics
Languages : en
Pages : 344
Book Description
Algebraic Theory of Quadratic Forms
Author: Manfred Knebusch
Publisher: Birkhäuser
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 60
Book Description
Publisher: Birkhäuser
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 60
Book Description