Adeles And Algebraic Groups

Author : A. Weil
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468491562

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Adeles and Algebraic Groups by A. Weil Pdf

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 : Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen
Publisher : Academic Press
Page : 614 pages
File Size : 41,9 Mb
Release : 1993-12-07
Category : Mathematics
ISBN : 0080874592

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Algebraic Groups and Number Theory by Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen Pdf

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 : André Weil
Publisher : Unknown
Page : 242 pages
File Size : 42,6 Mb
Release : 1961
Category : Adeles
ISBN : OCLC:221931457

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Adeles and Algebraic Groups by André Weil Pdf

Author : André Weil
Publisher : Unknown
Page : 121 pages
File Size : 41,7 Mb
Release : 1970
Category : Electronic
ISBN : OCLC:19008294

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Adeles and Algebraic Groups by André Weil Pdf

Author : André Weil
Publisher : Unknown
Page : 242 pages
File Size : 40,6 Mb
Release : 1961
Category : Group theory
ISBN : OCLC:1049272731

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Adeles and Algebraic Groups by André Weil Pdf

Author : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Publisher : Cambridge University Press
Page : 379 pages
File Size : 45,5 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9780521113618

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Algebraic Groups and Number Theory by Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk Pdf

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Author : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Publisher : Cambridge University Press
Page : 380 pages
File Size : 40,8 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9781009380652

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Algebraic Groups and Number Theory: Volume 1 by Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk Pdf

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 : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 227 pages
File Size : 55,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881611

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Automorphic Forms on Adele Groups. (AM-83), Volume 83 by Stephen S. Gelbart Pdf

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Author : V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 42,6 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9780821872888

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Algebraic Groups and Their Birational Invariants by V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski Pdf

Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 284 pages
File Size : 54,9 Mb
Release : 1975-03-21
Category : Mathematics
ISBN : 0691081565

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Automorphic Forms on Adele Groups by Stephen S. Gelbart Pdf

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Author : Nihon Sūgakkai
Publisher : MIT Press
Page : 1180 pages
File Size : 44,5 Mb
Release : 1993
Category : Mathematics
ISBN : 0262590204

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Encyclopedic Dictionary of Mathematics by Nihon Sūgakkai Pdf

V.1. A.N. v.2. O.Z. Apendices and indexes.

Author : Igor V. Nikolaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 52,5 Mb
Release : 2022-07-18
Category : Mathematics
ISBN : 9783110788815

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Noncommutative Geometry by Igor V. Nikolaev Pdf

Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.

Author : J. S. Milne
Publisher : Cambridge University Press
Page : 665 pages
File Size : 45,9 Mb
Release : 2017-09-21
Category : Mathematics
ISBN : 9781107167483

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Algebraic Groups by J. S. Milne Pdf

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 40,6 Mb
Release : 1966
Category : Group theory
ISBN : OCLC:610661807

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Algebraic Groups and Discontinuous Subgroups by Anonim Pdf

Author : William Joseph Haboush Brian Parshall
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 48,8 Mb
Release : 1994-05-02
Category : Electronic
ISBN : 0821868276

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Algebraic groups and their generalizations: Classical methods by William Joseph Haboush Brian Parshall Pdf