Algebraic Groups And Number Theory Volume 1

Author : Vladimir Platonov
Publisher : Cambridge University Press
ISBN 13 : 1009380656
Total Pages : 380 pages
Book Rating : 4.52/5 ( download)

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Download or read book Algebraic Groups and Number Theory: Volume 1 written by Vladimir Platonov and published by Cambridge University Press. This book was released on 2023-08-31 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

Author : Vladimir Platonov
Publisher : Academic Press
ISBN 13 : 9780080874593
Total Pages : 614 pages
Book Rating : 4.92/5 ( download)

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Download or read book Algebraic Groups and Number Theory written by Vladimir Platonov and published by Academic Press. This book was released on 1993-12-07 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

Author : Vladimir Petrovich Platonov
Publisher :
ISBN 13 : 9781139017756
Total Pages : 0 pages
Book Rating : 4.56/5 ( download)

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Download or read book Algebraic Groups and Number Theory written by Vladimir Petrovich Platonov and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first volume of a two-volume book that offers an in-depth, and essentially self-contained, treatment of the arithmetic theory of algebraic groups. It is accessible to graduate students and researchers in number theory, algebraic geometry, and related areas"--

Author :
Publisher :
ISBN 13 : 9781108596473
Total Pages : pages
Book Rating : 4.79/5 ( download)

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Download or read book ALGEBRAIC GROUPS AND NUMBER THEORY written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A. Weil
Publisher : Springer Science & Business Media
ISBN 13 : 1468491563
Total Pages : 137 pages
Book Rating : 4.62/5 ( download)

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Download or read book Adeles and Algebraic Groups written by A. Weil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the original lecture notes presented by A. Weil in which the concept of adeles was first introduced, in conjunction with various aspects of C.L. Siegel’s work on quadratic forms. Serving as an introduction to the subject, these notes may also provide stimulation for further research.

Author : Ian Stewart
Publisher : Springer
ISBN 13 : 9780412138409
Total Pages : 257 pages
Book Rating : 4.09/5 ( download)

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Download or read book Algebraic Number Theory written by Ian Stewart and published by Springer. This book was released on 1979-05-31 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title of this book may be read in two ways. One is 'algebraic number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a proper coverage of either topic would require more space than is available, and demand more of the reader than we wish to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without ever defining an abstract vector space: nor is there anything to suggest that they suf fered thereby. This historical fact may indicate that abstrac tion is not always as necessary as one commonly imagines; on the other hand the axiomatization of mathematics has led to enormous organizational and conceptual gains.

Author : T.A. Springer
Publisher : Springer Science & Business Media
ISBN 13 : 0817648402
Total Pages : 334 pages
Book Rating : 4.04/5 ( download)

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Download or read book Linear Algebraic Groups written by T.A. Springer and published by Springer Science & Business Media. This book was released on 2010-10-12 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.

Author : P. Slodowy
Publisher : Springer
ISBN 13 : 3540381910
Total Pages : 187 pages
Book Rating : 4.14/5 ( download)

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Download or read book Simple Singularities and Simple Algebraic Groups written by P. Slodowy and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : James E. Humphreys
Publisher : Springer Science & Business Media
ISBN 13 : 1468494430
Total Pages : 259 pages
Book Rating : 4.33/5 ( download)

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Download or read book Linear Algebraic Groups written by James E. Humphreys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3662029456
Total Pages : 556 pages
Book Rating : 4.59/5 ( download)

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Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.