The Geometry of Positive Quadratic Forms
Author: Sergeĭ Sergeevich Ryshkov
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 268
ISBN-13: 9780821830703
DOWNLOAD EBOOK →Papers and articles about quadratic forms.
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Computational Geometry of Positive Definite Quadratic Forms
Author: Achill Schurmann
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 183
ISBN-13: 082184735X
DOWNLOAD EBOOK →"Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, Minkowski's classical theory is presented, including an application to multidimensional continued fraction expansions. The reduction theories of Voronoi are described in great detail, including full proofs, new views, and generalizations that cannot be found elsewhere. Based on Voronoi's second reduction theory, the local analysis of sphere coverings and several of its applications are presented. These include the classification of totally real thin number fields, connections to the Minkowski conjecture, and the discovery of new, sometimes surprising, properties of exceptional structures such as the Leech lattice or the root lattices." "Throughout this book, special attention is paid to algorithms and computability, allowing computer-assisted treatments. Although dealing with relatively classical topics that have been worked on extensively by numerous authors, this book is exemplary in showing how computers may help to gain new insights."--BOOK JACKET.
Geometry of Positive Quadratic Forms
Author: Sergei Sergeevich Ryshkov
Publisher:
Published: 1982
Total Pages: 258
ISBN-13:
DOWNLOAD EBOOK →Quadratic Forms -- Algebra, Arithmetic, and Geometry
Author: Ricardo Baeza
Publisher: American Mathematical Soc.
Published: 2009-08-14
Total Pages: 424
ISBN-13: 0821846485
DOWNLOAD EBOOK →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.
The Algebraic and Geometric Theory of Quadratic Forms
Author: Richard S. Elman
Publisher: American Mathematical Soc.
Published: 2008-07-15
Total Pages: 456
ISBN-13: 9780821873229
DOWNLOAD EBOOK →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 Sensual (Quadratic) Form
Author: John Horton Conway
Publisher: Cambridge University Press
Published: 1997
Total Pages: 180
ISBN-13: 9780883850305
DOWNLOAD EBOOK →Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.
Quadratic Forms and Their Applications
Author: Eva Bayer-Fluckiger
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 330
ISBN-13: 0821827790
DOWNLOAD EBOOK →This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Geometric Methods in the Algebraic Theory of Quadratic Forms
Author: Oleg T. Izhboldin
Publisher: Springer
Published: 2004-02-07
Total Pages: 198
ISBN-13: 3540409904
DOWNLOAD EBOOK →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.
Quadratic Forms with Applications to Algebraic Geometry and Topology
Author: Albrecht Pfister
Publisher: Cambridge University Press
Published: 1995-09-28
Total Pages: 191
ISBN-13: 0521467551
DOWNLOAD EBOOK →A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Bilinear Algebra
Author: Kazimierz Szymiczek
Publisher: Routledge
Published: 2017-11-22
Total Pages: 496
ISBN-13: 1351464213
DOWNLOAD EBOOK →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.
