Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Geometric Methods in the Algebraic Theory of Quadratic Forms
Author | : Oleg T. Izhboldin,Bruno Kahn,Nikita A. Karpenko,Alexander Vishik |
Publsiher | : Springer |
Total Pages | : 198 |
Release | : 2004-02-07 |
Genre | : Mathematics |
ISBN | : 9783540409908 |
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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.
Geometric Methods in the Algebraic Theory of Quadratic Forms
Author | : Oleg T Tignol Jean-Pierre Izhboldin,Bruno Kahn,Nikita a Karpenko |
Publsiher | : Springer |
Total Pages | : 212 |
Release | : 2014-01-15 |
Genre | : Electronic Book |
ISBN | : 3662177749 |
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Geometric Methods in the Algebraic Theory of Quadratic Forms
![Geometric Methods in the Algebraic Theory of Quadratic Forms](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2004 |
Genre | : Algebraic fields |
ISBN | : LCCN:2004041647 |
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Geometric Methods in the Algebraic Theory of Quadratic Forms
![Geometric Methods in the Algebraic Theory of Quadratic Forms](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Oleg Tomovich Izhboldin |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2004 |
Genre | : Electronic Book |
ISBN | : OCLC:934111473 |
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Geometric Methods in the Algebraic Theory of Quadratic Forms
Author | : Anonim |
Publsiher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : 2004 |
Genre | : Forms, Pfister |
ISBN | : 3540207287 |
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The Algebraic and Geometric Theory of Quadratic Forms
Author | : Richard S. Elman,Nikita Karpenko,Alexander Merkurjev |
Publsiher | : American Mathematical Soc. |
Total Pages | : 456 |
Release | : 2008-07-15 |
Genre | : Mathematics |
ISBN | : 0821873229 |
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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
Author | : Ricardo Baeza |
Publsiher | : American Mathematical Soc. |
Total Pages | : 424 |
Release | : 2009-08-14 |
Genre | : Mathematics |
ISBN | : 9780821846483 |
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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.
Recent Advances in Real Algebraic Geometry and Quadratic Forms
Author | : Bill Jacob,Tsit-Yuen Lam |
Publsiher | : American Mathematical Soc. |
Total Pages | : 405 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9780821851548 |
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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.