國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Algebraic groups and number theory

Platonov, V. P. (1939-)

Algebraic groups and number theory

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algebraic groups and number theoryVladimir Platonov, Andrei Rapinchuk ; translated by Rachel Rowen.
作者:	Platonov, V. P.
其他作者:	Rapinchuk, A. S.
出版者:	Boston :Academic Press,c1994.
面頁冊數:	1 online resource (xi, 614 p.) :ill.
標題:	Algebriac number theory.
電子資源:	http://www.sciencedirect.com/science/book/9780125581806
ISBN:	9780125581806

Algebraic groups and number theory
Platonov, V. P.1939-

Algebraic groups and number theory[electronic resource] /Vladimir Platonov, Andrei Rapinchuk ; translated by Rachel Rowen. - Boston :Academic Press,c1994. - 1 online resource (xi, 614 p.) :ill. - Pure and applied mathematics ;v. 139. - Pure and applied mathematics (Academic Press) ;140..

Includes bibliographical references (p. 583-608) and index.

(Chapter Heading): Algebraic Number Theory. Algebraic Groups. Algebraic Groups over Locally Compact Fields. Arithmetic Groups and Reduction Theory. Adeles. Galois Cohomology. Approximation in Algebraic Groups. Class Numbers andClass Groups of Algebraic Groups. Normal Structure of Groups of Rational Points of Algebraic Groups. Appendix A. Appendix B: Basic Notation. -- Algebraic Number Theory: Algebraic Number Fields, Valuations, and Completions. Adeles and Ideles; Strong and Weak Approximation; The Local-Global Principle. Cohomology. Simple Algebras over Local Fields. Simple Algebras over Algebraic Number Fields. Algebraic Groups: Structural Properties of Algebraic Groups. Classification of K-Forms Using Galois Cohomology. The Classical Groups. Some Results from Algebraic Geometry. Algebraic Groups over Locally Compact Fields: Topology and Analytic Structure. The Archimedean Case. The Non-Archimedean Case. Elements of Bruhat-Tits Theory. Results Needed from Measure Theory. Arithmetic Groups and Reduction Theory: Arithmetic Groups. Overview of Reduction Theory: Reduction in GLn(R). Reduction in Arbitrary Groups. Group-Theoretic Properties of Arithmetic Groups. Compactness of GR/GZ. The Finiteness of the Volume of GR/GZ. Concluding Remarks on Reduction Theory. Finite Arithmetic Groups. Adeles: Basic Definitions. Reduction Theory for GA Relative to GK. Criteria for the Compactness and the Finiteness of Volume of GA/GK. Reduction Theory for S-Arithmetic Subgroups. Galois Cohomology: Statement of the Main Results. Cohomology of Algebraic Groups over Finite Fields. Galois Cohomology of Algebraic Tori. Finiteness Theorems for Galios Cohomology. Cohomology of Semisimple Algebraic Groups over Local Fields and Number Fields. Galois Cohomology and Quadratic, Hermitian, and Other Forms. Proof of Theorems 6.4 and 6.6: Classical Groups. Proof of Theorems 6.4 and 6.6: Exceptional Groups. Approximation in Algebraic Groups: Strong and Weak Approximation in Algebraic Varieties. The Kneser-Tits Conjecture. Weak Approximation in Algebraic Groups. The Strong Approximation Theorem. Generalization of the Strong Approximation Theorem. Class Numbers and Class Groups of Algebraic Groups: Class Numbers of Algebraic Groups and Number of Classes in a Genus. Class Numbers and Class Groups of Semisimple Groups of Noncompact Type; The Realization Theorem. Class Numbers of Algebraic Groups of Compact Type. Estimating the Class Number for Reductive Groups. The Genus Problem. Normal Subgroup Structure of Groups of Rational Points of Algebraic Groups: Main Conjecture and Results. Groups of Type An. The Classical Groups. Groups Split over a Quadratic Extension. The Congruence Subgroup Problem (A Survey). Appendices: Basic Notation. Bibliography. Index.

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.

ISBN: 9780125581806

Source: 81732:81732Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

536204
Algebriac number theory.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA3 / .P8 vol. 139eb

Dewey Class. No.: 512/.74

Algebraic groups and number theory
LDR:04815cmm 2200361Ia 4500 001 313568
003 OCoLC
005 20111122085749.0
006 m d
007 cr cn|||||||||
008 111229s1994 maua ob 001 0 eng d
020 $a 9780125581806
020 $a 0125581807
035 $a (OCoLC)316566783
035 $a ocn316566783
035 $a 313568
037 $a 81732:81732 $b Elsevier Science & Technology $n http://www.sciencedirect.com
040 $a OPELS $b eng $c OPELS $d OCLCQ $d OPELS $d OCLCQ
049 $a TEFA
050 4 $a QA3 $b .P8 vol. 139eb
050 4 $a QA247 $b .P53 1994eb
082 0 4 $a 512/.74 $2 22
100 1 $a Platonov, V. P. $q (Vladimir Petrovich), $d 1939- $3 536202
240 1 0 $a Algebraicheskie gruppy i teori�i�a chisel. $l English
245 1 0 $a Algebraic groups and number theory $h [electronic resource] / $c Vladimir Platonov, Andrei Rapinchuk ; translated by Rachel Rowen.
260 $a Boston : $b Academic Press, $c c1994.
300 $a 1 online resource (xi, 614 p.) : $b ill.
490 1 $a Pure and applied mathematics ; $v v. 139
504 $a Includes bibliographical references (p. 583-608) and index.
505 0 $a (Chapter Heading): Algebraic Number Theory. Algebraic Groups. Algebraic Groups over Locally Compact Fields. Arithmetic Groups and Reduction Theory. Adeles. Galois Cohomology. Approximation in Algebraic Groups. Class Numbers andClass Groups of Algebraic Groups. Normal Structure of Groups of Rational Points of Algebraic Groups. Appendix A. Appendix B: Basic Notation. -- Algebraic Number Theory: Algebraic Number Fields, Valuations, and Completions. Adeles and Ideles; Strong and Weak Approximation; The Local-Global Principle. Cohomology. Simple Algebras over Local Fields. Simple Algebras over Algebraic Number Fields. Algebraic Groups: Structural Properties of Algebraic Groups. Classification of K-Forms Using Galois Cohomology. The Classical Groups. Some Results from Algebraic Geometry. Algebraic Groups over Locally Compact Fields: Topology and Analytic Structure. The Archimedean Case. The Non-Archimedean Case. Elements of Bruhat-Tits Theory. Results Needed from Measure Theory. Arithmetic Groups and Reduction Theory: Arithmetic Groups. Overview of Reduction Theory: Reduction in GLn(R). Reduction in Arbitrary Groups. Group-Theoretic Properties of Arithmetic Groups. Compactness of GR/GZ. The Finiteness of the Volume of GR/GZ. Concluding Remarks on Reduction Theory. Finite Arithmetic Groups. Adeles: Basic Definitions. Reduction Theory for GA Relative to GK. Criteria for the Compactness and the Finiteness of Volume of GA/GK. Reduction Theory for S-Arithmetic Subgroups. Galois Cohomology: Statement of the Main Results. Cohomology of Algebraic Groups over Finite Fields. Galois Cohomology of Algebraic Tori. Finiteness Theorems for Galios Cohomology. Cohomology of Semisimple Algebraic Groups over Local Fields and Number Fields. Galois Cohomology and Quadratic, Hermitian, and Other Forms. Proof of Theorems 6.4 and 6.6: Classical Groups. Proof of Theorems 6.4 and 6.6: Exceptional Groups. Approximation in Algebraic Groups: Strong and Weak Approximation in Algebraic Varieties. The Kneser-Tits Conjecture. Weak Approximation in Algebraic Groups. The Strong Approximation Theorem. Generalization of the Strong Approximation Theorem. Class Numbers and Class Groups of Algebraic Groups: Class Numbers of Algebraic Groups and Number of Classes in a Genus. Class Numbers and Class Groups of Semisimple Groups of Noncompact Type; The Realization Theorem. Class Numbers of Algebraic Groups of Compact Type. Estimating the Class Number for Reductive Groups. The Genus Problem. Normal Subgroup Structure of Groups of Rational Points of Algebraic Groups: Main Conjecture and Results. Groups of Type An. The Classical Groups. Groups Split over a Quadratic Extension. The Congruence Subgroup Problem (A Survey). Appendices: Basic Notation. Bibliography. Index.
520 $a 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.
588 $a Description based on print version record.
650 0 $a Algebriac number theory. $3 536204
650 0 $a Linear algebraic groups. $3 191020
650 6 $a Groupes lin�eaires alg�ebriques. $3 536205
650 6 $a Nombres alg�ebriques, Th�eorie des. $3 536206
650 7 $a Nombres alg�ebriques, th�eorie des. $2 ram $3 536207
655 4 $a Electronic books. $2 local. $3 214472
700 1 $a Rapinchuk, A. S. $q (Andre�i Stepanovich) $3 536203
776 0 8 $i Print version: $a Platonov, V. P. (Vladimir Petrovich), 1939- $s Algebraicheskie gruppy i teori�i�a chisel. English. $t Algebraic groups and number theory. $d Boston : Academic Press, c1994 $z 0125581807 $z 9780125581806 $w (DLC) 92035876 $w (OCoLC)26928645
830 0 $a Pure and applied mathematics (Academic Press) ; $v 140. $3 441190
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/book/9780125581806
994 $a C0 $b TEF