Algebraic Groups And Number Theory Volume 1

Author : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Publisher : Cambridge University Press
Page : 380 pages
File Size : 43,5 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 : Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen
Publisher : Academic Press
Page : 614 pages
File Size : 45,7 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 : Vladimir Petrovich Platonov,Andreĭ Stepanovich Rapinchuk,Igor Rapinchuk
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 2023
Category : Linear algebraic groups
ISBN : 1139017756

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Algebraic Groups and Number Theory by Vladimir Petrovich Platonov,Andreĭ Stepanovich Rapinchuk,Igor Rapinchuk Pdf

"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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 1108596479

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ALGEBRAIC GROUPS AND NUMBER THEORY by Anonim Pdf

Author : A. Weil
Publisher : Springer Science & Business Media
Page : 137 pages
File Size : 52,7 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 : Armand Borel
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209416

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Linear Algebraic Groups by Armand Borel Pdf

This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.

Author : P. Slodowy
Publisher : Springer
Page : 187 pages
File Size : 52,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540381914

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Simple Singularities and Simple Algebraic Groups by P. Slodowy Pdf

Author : T.A. Springer
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 48,7 Mb
Release : 2010-10-12
Category : Mathematics
ISBN : 9780817648404

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Linear Algebraic Groups by T.A. Springer Pdf

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 : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Publisher : Cambridge University Press
Page : 379 pages
File Size : 52,7 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 : James E. Humphreys
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494433

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Linear Algebraic Groups by James E. Humphreys Pdf

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 : Andre Weil
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642619458

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Basic Number Theory by Andre Weil Pdf

From the reviews: "L.R. Shafarevich showed me the first edition [...] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH

Author : J. S. Milne
Publisher : Cambridge University Press
Page : 665 pages
File Size : 53,6 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 : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 53,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

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.

Author : M.E. Pohst
Publisher : Birkhäuser
Page : 99 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885898

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Computational Algebraic Number Theory by M.E. Pohst Pdf

Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction • Topics from finite fields • Arithmetic and polynomials • Factorization of polynomials • Topics from the geometry of numbers • Hermite normal form • Lattices • Reduction • Enumeration of lattice points • Algebraic number fields • Introduction • Basic Arithmetic • Computation of an integral basis • Integral closure • Round-Two-Method • Round-Four-Method • Computation of the unit group • Dirichlet's unit theorem and a regulator bound • Two methods for computing r independent units • Fundamental unit computation • Computation of the class group • Ideals and class number • A method for computing the class group • Appendix • The number field sieve • KANT • References • Index

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 49,9 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9780387499222

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Number Theory by Henri Cohen Pdf

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.