Quadratic Forms And Their Applications
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Quadratic Forms And Their Applications
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Author : Eva Bayer-Fluckiger
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Quadratic Forms And Their Applications written by Eva Bayer-Fluckiger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Specialization Of Quadratic And Symmetric Bilinear Forms
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Author : Manfred Knebusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-22
Specialization Of Quadratic And Symmetric Bilinear Forms written by Manfred Knebusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-22 with Mathematics categories.
A Mathematician Said Who Can Quote Me a Theorem that’s True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It is—poetic exaggeration allowed—a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has “good reduction” with respect to? (see§1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of?. The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of Izhboldin–Kahn–Karpenko–Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there).
Geometric Methods In The Algebraic Theory Of Quadratic Forms
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Author : Oleg T. Izhboldin
language : en
Publisher: Springer
Release Date : 2004-02-07
Geometric Methods In The Algebraic Theory Of Quadratic Forms written by Oleg T. Izhboldin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-07 with Mathematics categories.
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
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Author : Albrecht Pfister
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-28
Quadratic Forms With Applications To Algebraic Geometry And Topology written by Albrecht Pfister and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-28 with Mathematics categories.
A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Quadratic Forms
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Author : Michael Barot
language : en
Publisher: Springer
Release Date : 2019-01-28
Quadratic Forms written by Michael Barot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-28 with Mathematics categories.
This monograph presents combinatorial and numerical issues on integral quadratic forms as originally obtained in the context of representation theory of algebras and derived categories. Some of these beautiful results remain practically unknown to students and scholars, and are scattered in papers written between 1970 and the present day. Besides the many classical results, the book also encompasses a few new results and generalizations. The material presented will appeal to a wide group of researchers (in representation theory of algebras, Lie theory, number theory and graph theory) and, due to its accessible nature and the many exercises provided, also to undergraduate and graduate students with a solid foundation in linear algebra and some familiarity on graph theory.
Bilinear Algebra
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Author : Kazimierz Szymiczek
language : en
Publisher: Routledge
Release Date : 2017-11-22
Bilinear Algebra written by Kazimierz Szymiczek and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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.
Quadratic And Higher Degree Forms
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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Quadratic And Higher Degree Forms written by Krishnaswami Alladi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Quaternion Algebras
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Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28
Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
The Sensual Quadratic Form
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Author : John Horton Conway
language : en
Publisher: Cambridge University Press
Release Date : 1997
The Sensual Quadratic Form written by John Horton Conway and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.
Binary Quadratic Forms
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Author : Johannes Buchmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-22
Binary Quadratic Forms written by Johannes Buchmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-22 with Mathematics categories.
The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. The book explains applications to cryptography and requires only basic mathematical knowledge. The author is a world leader in number theory.