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Author: Albrecht Pfister
Publisher: Cambridge University Press
ISBN: 0521467551
Category : Mathematics
Languages : en
Pages : 191
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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.
Author: Albrecht Pfister
Publisher: Cambridge University Press
ISBN: 0521467551
Category : Mathematics
Languages : en
Pages : 191
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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.
Author: Bill Jacob
Publisher: American Mathematical Soc.
ISBN: 0821851543
Category : Mathematics
Languages : en
Pages : 405
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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.
Author: Eva Bayer-Fluckiger
Publisher: American Mathematical Soc.
ISBN: 0821827790
Category : Mathematics
Languages : en
Pages : 311
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Book Description
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.
Author: Ricardo Baeza
Publisher: American Mathematical Soc.
ISBN: 0821846485
Category : Mathematics
Languages : en
Pages : 424
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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.
Author: Richard S. Elman
Publisher: American Mathematical Soc.
ISBN: 9780821873229
Category : Mathematics
Languages : en
Pages : 456
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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.
Author: Skip Garibaldi
Publisher: Springer
ISBN: 9781461426301
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Surveys.- Multiples of forms.- On Saltman's p-Adic Curves Papers.- Serre's Conjecture II: A Survey.- Field Patching, Factorization, and Local-Global Principles.- Deformation Theory and Rational Points on Rationally Connected Varieties.- Recent Progress on the Kato Conjecture.- Elliptic Curves and Iwasawa's μ = 0 Conjecture.- Cohomological Invariants of Central Simple Algebras with Involution.- Witt Groups of Varieties and the Purity Problem.- Invited articles.- Some Extensions and Applications of the Eisenstein Irreducibility Criterion.- On the Kernel of the Rost Invariant for E8 Modulo 3.- Une version du théorème d'Amer et Brumer pour les zéro-cycles.- Quaternion Algebras with the Same Subfields.- Lifting of Coefficients for Chow Motives of Quadrics.- Upper Motives of Outer Algebraic Groups.- Triality and étale algebras.- Remarks on Unimodular Rows.- Vector Bundles Generated by Sections and Morphisms to Grassmannians.- Adams Operations and the Brown-Gersten-Quillen Spectral Sequence.- Non-self-dual Stably Free Modules.- Homotopy Invariance of the Sheaf WNis and of Its Cohomology.- Imbedding Quasi-split Groups in Isotropic Groups.
Author: Kazimierz Szymiczek
Publisher: Routledge
ISBN: 1351464213
Category : Mathematics
Languages : en
Pages : 496
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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.
Author: Sergeĭ Mikhaĭlovich Nikolʹskiĭ
Publisher: American Mathematical Soc.
ISBN: 9780821830925
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Papers about algebraic geometry and their applications.
Author: Tsit-Yuen Lam
Publisher: Addison-Wesley
ISBN: 9780805356663
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Author: Achill Schurmann
Publisher: American Mathematical Soc.
ISBN: 082184735X
Category : Discrete geometry
Languages : en
Pages : 183
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Book Description
"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.
