Algebraic Groups and Number Theory

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Academic Press, Dec 7, 1993 - Mathematics - 614 pages
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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.
 

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Contents

Chapter 1 Algebraic number theory
1
Chapter 2 Algebraic Groups
47
Chapter 3 Algebraic Groups over Locally Compact Fields
107
Chapter 4 Arithmetic Groups and Reduction Theory
171
Chapter 5 Adeles
243
Chapter 6 Galois cohomology
281
Chapter 7 Approximation in Algebraic Groups
399
Chapter 8 Class numbers and class groups of algebraic groups
439
Chapter 9 Normal subgroup structure of groups of rational points of algebraic groups
509
Appendix A
571
Appendix B Basic Notation
579
Bibliography
583
Index
609
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