Download or read book The Algebraic and Geometric Theory of Quadratic Forms written by Richard S. Elman and published by American Mathematical Soc.. This book was released on 2008-07-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic and Arithmetic Theory of Quadratic Forms written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2004 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
Download or read book Compositions of Quadratic Forms written by Daniel B. Shapiro and published by Walter de Gruyter. This book was released on 2000 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Compositions of Quadratic Forms".
Download or read book Quadratic and Hermitian Forms written by W. Scharlau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the well-known books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object - the Witt ring - then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems.
Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Methods in the Algebraic Theory of Quadratic Forms written by and published by Springer Science & Business Media. This book was released on 2004 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book K Theory and Algebraic Geometry Connections with Quadratic Forms and Division Algebras written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of two - also available in a set of both volumes.
Download or read book Introduction to Quadratic Forms over Fields written by T.Y. Lam and published by American Mathematical Soc.. This book was released on with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quadratic and Hermitian Forms written by McMaster University and published by American Mathematical Soc.. This book was released on 1984 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2005 with total page 1512 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quadratic Forms Linear Algebraic Groups and Cohomology written by Skip Garibaldi and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Basic Quadratic Forms written by Larry J. Gerstein and published by American Mathematical Soc.. This book was released on 2008 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics--particularly group theory and topology--as well as to cryptography and coding theory. This book is a self-contained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest--with special attention to the theory over the integers and over polynomial rings in one variable over a field--and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Download or read book Quadratic Forms with Applications to Algebraic Geometry and Topology written by Albrecht Pfister and published by Cambridge University Press. This book was released on 1995-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Download or read book The Book of Involutions written by Max-Albert Knus and published by American Mathematical Soc.. This book was released on 1998-06-30 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings
Download or read book Cohomological Invariants Exceptional Groups and Spin Groups written by Skip Garibaldi and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2003 with total page 1418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
