Platonov V., Rapinchuk A. — Algebraic groups and number theory :: Электронная библиотека попечительского совета мехмата МГУ

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

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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:

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

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Предметный указатель

Morphism, dominant      96
Morphism, K-      49
Mostow’s Theorem      124 127
Multidimensional conjugacy classes      10
Multinorm principle      313
Multinorm torus      54
Multiplicative arithmetic method      536
Nakayama — Tate theorem, global version      283
Nakayama — Tate theorem, local version      282
Natural structure      285
Noether’s theorem      143
Non-Abelian cohomology      21
Non-singular points      see “Simple points”
Noncompact type      205
Norm torus      54
Normal subgroups, standard description of      537
One-parameter subgroups      54
Order      42
Order, maximal      42
Orthogonal group      80
Ostrowski’s theorem      3
Outer form      66
Parabolic subgroup      57
Parabolic subgroup, standard      62
Parahoric subgroup      149
Platonov — Bondarenko — Rapinchuk theorem      487
Platonov — Yanchevskii theorem      30
Platonov’s conjecture on arithmeticity      437
Platonov’s conjecture on projective simplicity      510
Platonov’s theorem      407 414 426
Polar decomposition      124 126
Prasad — Margulis theorem      516
Prasad — Raghunathan theorem      35 411
Pro-p-group      138
Product formula      12
Product, restricted topological      161
Profinite group      137
Projective limit      137
Projective system      137
Pseudobase      42
Quasisplit      58
Quotient varieties      52
Radical      58
Radical, unipotent      58
Ramification group      10
Ramification index      5
Rank, K-      65
Rapinchuk theorem      569
Real cohomology      320
Realization Theorem      452
Reduced norm      27
Reduction      142
Reduction, in $GL_n(\mathbb{R})$       175
Reduction, in arbitrary groups      189
Reduction, map      143
Reduction, smooth      142
Reduction, theory      175
Reduction, theory, for S-arithmetic subgroups      266
Reductive group      58
Relative root systems      65
Residue, degree      5
Residue, field      5
Residue, skew field      29
Restriction, map      19
Restriction, of scalars      49
Riehm’s theorem      114
Rohlf’s theorem      490
Root, subgroup      353 547
Root, system      59
Schur multiplier      17 312
Self-adjoint group      124
Semisimple group      58
Serre congruence subgroup conjecture      264
Shafarevich — Tate group      284 323
Shapiro’s Lemma      20
Shapiro’s Lemma, noncommutative version      25
Siegel set      177 215
Simple group      62
Simple point of reduction      142
Simple points      97
Simply connected      62

Singular points      97
Skolem — Noether theorem      27
Special covering      76
Special linear group      78
Special unitary group      84
Spinor group      82
Splitting field      27 53
Stabilizer      44 45
Standard description of normal subgroups      537
Standard parabolic subgroup      62
Steinberg’s theorem      338 342
Strong approximation theorem      427
Strong approximation theorem, for a field      14
Strong Hasse principle      347
Symplectic group      80
System of simple roots      59
Table of the centers of simple groups      64
Tamagawa measure      261
Tamagawa number      262 266
Tanaka — Artin problem      27
Tangent space      97
Tate cohomology      300
Tate’s theorem      302 307 308
Theorem on the stabilizer      444
Theorems on finiteness of orbits      268
Tits, index      66
Tits, system      149
Tits, theorem      406
Topology, adele      11
Topology, arithmetic      555
Topology, congruence      555
Topology, idele      12
Topology, v-adic      108
Toric varieties      104
Torus, K-anisotropic      53
Torus, multinorm      54
Torus, norm      54
Torus, quasisplit      55
Transgression map      19
Truncated exponential map      56
Truncated logarithmic map      56
Twisting      23 68
Uniformizing parameter      5 29
Unimodular group      160
Unipotent radical      58
Unirational K-varieties      98
Unitary group      84
Universal covering      63
Universal covering, defined over K      76
Unramified cohomology      294
v-adic topology      108
Valuation      2
Valuation, archimedean      2
Valuation, complex      4
Valuation, equivalent      3
Valuation, extension of      4
Valuation, ideal      5
Valuation, logarithmic      2
Valuation, non-archimedean      2
Valuation, normalized      12
Valuation, p-adic      2
Valuation, real      4
Valuation, ring      5
Variety, defined over K      96
Variety, maximal toric      104
Variety, of Borel subgroups      106
Variety, of n-dimensional characters      435
Variety, of representations      103
Variety, rational      98
Variety, smooth      98
Variety, toric      104
Vertex, distinguished      66
Volume, criterion for finite, of       260
Volume, criterion for finite, of $G_{\mathbb{R}}/G_{\mathbb{Z}}$       213
Wang’s theorem      38
Weak approximation theorem for a fiel      218
Wedderburn’s theorem      288
Weyl group      59 65 149
Whitehead group, reduced      27
Whitney’s theorem      119
Witt index      82
Witt’s Theorem      92 545

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