Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Platonov V., Rapinchuk A. — Algebraic groups and number theory
Platonov V., Rapinchuk A. — Algebraic groups and number theory



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Algebraic groups and number theory

Авторы: Platonov V., Rapinchuk A.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 614

Добавлена в каталог: 25.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
(Sylow) pro-q-subgroup      139
Absolute rank      57
Absolutely simple group      62
Actions of algebraic groups on varieties      99
Additive Jordan decomposition      52
Adele group      249
Adele group, cohomology of      297
Adele group, finite      250
Adele group, integral      244 249
Adele group, principal      249
Adele group, principal 5-      250
Adele group, S-      249
Adele group, S-integral      249
Adele group, T-integral S-      250
Adele ring      10
Adele ring, 5-integral      11
Adele ring, integral      11
Adele ring, principal      11
Adele space      243
Adele space, principal      244
Adele space, S-integral      244
Adele topology      11
Adeles      10 243
Adelization of a regular K-map      244
Adjoint representation      51
Algebraic group      47
Algebraic group, adjoint      62
Algebraic group, character of      52
Algebraic group, classical simply connected simple algebraic K-groups, list of      92
Algebraic group, classification of K-forms of      75
Algebraic group, diagonalizable      52
Algebraic group, K-split      52 57 58
Algebraic group, quasisplit      58
Algebraic group, reductive      58
Algebraic group, semisimple      58
Algebraic group, simple      62
Algebraic group, simply connected      62
Algebraic group, unipotent      56
Algebraic number field      1
Algebraic tori      52
Analytic structure      110
Anisotropic groups, K-      65
Anisotropic kernel      67
Anisotropic torus, K-      53
Approximation, absolute strong      250
Approximation, strong      13 250 399
Approximation, strong, in groups, criterion for      427
Approximation, strong, theorem      427
Approximation, strong, theorem for a field      14
Approximation, weak      13 399
Approximation, weak, in algebraic groups      415
Approximation, weak, theorem for a field      14
Arithmetic subgroup      171
Arithmetic subgroup, O-      227
Arithmetic subgroup, S-      175 267 268
Arithmetic topology      555
Arithmeticity, conjecture on      437
B-N pair      149
Bartels — Kitaoka theorem      234
Bartels’ problem      309
Bartels’ theorem      492
Behr’s theorem      152
Birational isomorphism      98
Borel — Harish — Chandra theorem      193
Borel, measure      159
Borel, subgroups      57
Brauer group      28
Brauer — Hasse — Noether theorem      38
Bruhat decomposition      60
Building      149
Cartan decomposition      150
Cayley — Dickson parametrization      403
Central isogeny      62
Centralizer theorem      448
Chebotarev density theorem      9
Chernousov’s theorem      387
Chevalley base      64
Chevalley group      65
Chevalley’s theorem      99
Chevalley’s theorem, stronger version      100
class      444 449
Class group      452
Class number      2 251 440
Class number, in the genus      444 448 449
Class number, in the genus, of a quadratic form      447
Class number, in the genus, of an element      448
Class number, in the genus, of lattices in the full matrix algebra under conjugation      465
Closed Orbit Lemma      99
Coboundary map      23
Cohomological dimension      340
Cohomology      16
Cohomology, continuous      20
Cohomology, Galois      21
Cohomology, non-Abelian      21
Cohomology, of adele groups      297
Cohomology, of algebraic groups      71
Cohomology, of groups of w-adic integral points      292
Cohomology, real      320
Cohomology, Tate      300
Cohomology, unramified      294
Commensurability subgroup      206
Compact type      205
Compactly presented group      152
Compactness, criterion for , of $G_{\mathbb{R}}/G_{\mathbb{R}}$      207
Compactness, criterion for of $G_A/G_K$      260
Completion      3
Congruence, kernel      555
Congruence, subgroup      31 134 172 553
Congruence, subgroup conjecture (of Serre)      556
Congruence, subgroup problem      553
Congruence, theorem      525
Congruence, topology      555
Connected component      51
Continuous cohomology      20
Convergence coefficients      261
Corestriction map      20
Decomposition group      6
Decomposition, Bruhat      60
Decomposition, Cartan      150
Decomposition, Iwasawa, for $GL_n(\mathbb{R})$      129
Decomposition, Iwasawa, theorem      131
Decomposition, Jordan      52
Decomposition, Jordan, additive      52
Decomposition, Levi      58
Decomposition, polar      124 126
Degree of an algebraic group      48
Degree, residue      5
Density Theorem, Borel      205
Density Theorem, Chebotarev      9
Diagonalizable algebraic group      52
Dieudonne’ determinant      39
Differential form      165
Differential form, integrating      165
Differential form, invariant      165
Dirichlet unit theorem      209
Distinguished vertex      66
Dominant morphism      96
E.Cartan’s theorem      407
Eichler’s theorem      38
Eichler’s theorem, unitary version      360
Eisenstein polynomial      9
Exponential map      116
Exponential map, truncated      56
Extension, K-adequate      309
Extension, totally ramified      5
Extension, totally real      229
Extension, unramified      5
Field, algebraic number      1
Field, local      5
Field, local, non-archimedean      5
Field, of definition of an algebraic variety      96
Field, of type (F)      316
Field, residue      5
Field, splitting      27 53
Field, Weak approximation theorem for a      14
Finite presentability of S-arithmetic groups      272
Finiteness theorem for the orbits of arithmetic groups      193
Forms, differential      165
Forms, inner      66
Forms, integrating differential      165
Forms, invariant differential      165
Forms, K-forms of algebraic groups, classification of      75
Forms, Killing      51
Forms, L/K-      67
Forms, outer      66
Fractional ideals      2
Frobenius automorphism      6
Fundamental domain      163
Fundamental group      63
Fundamental set      164 189 193 253 267
Galois cohomology      21
Generalized Dirichlet’s theorem      276
Generalized Siegel set      224
Genus      444 449
Genus problem      494
Genus problem, for integral representations      504
Genus problem, in arithmetic groups      494
Grothendieck’s problem      434
Group, absolutely simple      62
Group, adele      see “Adele group”
Group, algebraic      47
Group, algebraic, haracter of      52
Group, classification of semisimple groups      63
Group, compactly presented      152
Group, conjugacy separable      502
Group, decomposition      6
Group, defined over K      see “Group K-”
Group, ideal class      1 2
Group, inertia      10
Group, isogeneous      56
Group, K-      49
Group, K-anisotropic      65
Group, K-isotropic      65
Group, of cocharacters      see “One-parameter subgroups”
Group, of compact type      228
Group, of mixed type      228
Group, of noncompact type      228
Group, of S-units      267
Group, of type (F)      316
Group, of units      171
Group, orthogonal      80
Group, pro-p-      138
Group, profinite      137
Group, ramification      10
Group, reductive      58
Group, self-adjoint      124
Group, semisimple      58
Group, simple      62
Group, special linear      78
Group, special unitary      84
Group, spinor      82
Group, symplectic      80
Group, unimodular      160
Group, unitary      84
Group, with bounded generation      203
Haar measure      159
Haar measure, on a finite direct product      160
Harish — Chandra’s theorem      183
Hasse norm principle      15 307
Hasse norm theorem      308
Hasse principle      284 285
Hasse principle, first obstruction to      309
Hasse principle, for cohomology of arithmetic subgrou simply connected groups      491
Hasse principle, for simply connected groups      286
Hasse principle, for tori      307
Hasse principle, strong      347
Hasse principle, total obstruction to      311
Hasse principle, weak      347
Hasse — Witt invariant      349
Hensel’s Lemma      143
Hermite’s theorem      9
Hilbert class field      443
Hilbert’s Theorem 90      70
Hochschild — Serre spectral sequence      19
Hochschild — Serre spectral sequence, for non-Abelian cohomology      25
Ideal class group      1 2
Idele topology      12
Ideles      10
Ideles, group of      11
Ideles, group of, integral      12
Ideles, group of, principal      12
Ideles, group of, S-integral      12
Ideles, group of, special      12
INDEX      27
Inertia group      10
Inflation map      19
Inner form      66
Invariant, differential form      165
Invariant, Hasse — Witt      349
Invariant, measure on a quotient space      162
Invariant, of a division algebra      29
Invariant, of a simple algebra      29
Inverse function theorem      110
Inverse limit      137
Inverse system      137
Involution      83
Involution, of the first kind      83
Involution, of the first type      85
Involution, of the second kind      83
Involution, of the second type      85
Isogeny      56 62
Iwahori subgroup      148
Iwasawa decomposition for $GL_n(\mathbb{R})$      129
Iwasawa decomposition theorem      131
Jordan decomposition      52
Killing form      51
Kneser — Tits conjecture      406
Kneser’s theorem      462
Krasner’s lemma, unitary version      364
Landherr’s theorem      359
Lang’s isogeny theorem      290
Lang’s theorem      281
Lattice (on a vector space)      42
Lattice (on a vector space), criterion for free      442
Lattice (on a vector space), in a locally compact topological group      221
Lattice (on a vector space), local      42
Levi decomposition      58
Lie algebra of an algebraic group      51
Lie algebra of an analytic group      116
Lie subgroup      117
Local field      5
Local field, non-archimedean      5
Local lattice      42
Local-global principle      14 285
Logarithmic map      116
Logarithmic map, truncated      56
Mahler’s criterion      211
Margulis’ conjecture      511
Margulis’ theorem      517
Matsumoto’s theorem      139
Measure      159
Metaplectic conjecture, weak      532 560
Metaplectic kernel      557
Meyer’s theorem      342
Minkowski — Hasse Theorem      14
Minkowski’s lemma      232 493
Mixed type      205
Module of a group      160
Module of an automorphism      159
Morphism of algebraic groups      48
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте