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Waterhouse W.C. — Introduction to Affine Group Schemes, Vol. 66
Waterhouse W.C. — Introduction to Affine Group Schemes, Vol. 66

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Название: Introduction to Affine Group Schemes, Vol. 66

Автор: Waterhouse W.C.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 180

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$F_{k'}$      11
$G^0$      51
$G^D$      17
$G_a$, $G_m$, $\alpha_p$, $\mu_p$      3
$H^1$      136—137
$S^{-1}R$, $R_f$, $R_P$      152
$\Delta$, $\epsilon$, S      8
$\Lambda^rV$      152
$\mathscr{F}(G)$      73
$\Omega_{A/k}$      83
$\pi_o(A)$, $\pi_o(X)$      49
Action of an affine group scheme      21
Adjoint representation of G      100
Affine algebraic group      29
Affine group scheme      5
Algebra      3
Algebraic affine group scheme      24
Algebraic matrix group      29
Anisotropic torus      56
Anti-equivalence      15
Antipode      8
Arf invariant      147
Artin — Schreier theory      143
Augmentation ideal      13
Aut(M)      58
Automorphism group scheme      58
Base change      11
Borel subgroup      77
Carder duality      17
Cartan subgroup      77
Center of a group scheme      27
Central simple algebra      145
CHARACTER      14
Charater group      55
Clopen set      42
Closed embedding      13
Closed set in $k^n$      28
Closed set in Spec A      42
Closed set, closure      156
Closed subgroup      13
Coalgebra      26
Coassociativity      9
Cocommutative Hopf algebra      10
Coconnected Hopf algebra      64
Cocycle      136 137
Cohomology class      136 137
Cokernel      127
Commutative Lie algebra      99
Comodule      23
Connected affine group scheme      51
Connected component of G      51
Connected set, connected component      157
Constant group scheme      16 45
Continuous $\mathscr{G}$-action      48
Continuous function      157
Coseparable coalgebra      53
Crossed homomorphism      137
Dense set      157
Deploye      see Split
Derivation      83
Derived group      73
Descent data      131
Diagonalizable group scheme      14
Differential field      77
Differential operator      99
Differentials of an algebra      84
Dimension of an algebraic G      88
Direct limit      151
Distribution (supported at e)      99
Dual      see Carrier duality
Etale finite group scheme      49 91
Etale topology      118
Exterior power      152
Faithfully flat (fpqc) topology      117
Faithfully flat covering      117
Faithfully flat ring map      103
Fiber product      7
Finite group scheme      16
Fixed element      64
Flat ring inap      103
FORM      see Twisted form
Formal group law, formal group, formal Lie group      90
Formally principal homogeneous space      142
fppf topology      118
Frobenius homomorphism      91
functor      4
Grothendieck topology      118
Group scheme of units of D      57
Group-like element      14
Height one, finite group of      87
Hilbert basis theorem      153
Hom(G,H)      18
Homomorphism of group schemes      13
Hopf algebra      8
Hopf ideal      13
Ideal in a Lie algebra      99
Idempotent      19
Invariant operator      92
Inverse limit      151
Invertible module      149
Irreducible representation      63
Irreducible set, irreducible component      39 40
Isogeny      119
Jacobi identity      93
Jordan decomposition      69
Kernel of a group scheme map      14
Kolchin fixed point theorem      62
Krull intersection theorem      154
Kunuher theory      143
k[G]      32 32
Lie algebra      93
Lie — Koichin triangularization theorem      74
Lie(G)      92
Linear algebraic group defined over k      33
Linear representation      21
Local ring      153
localization      152
Maximal ideal      153
Multiplicative type, group of      55
Nakayama's lemma      154
Natural correspondence      6
Natural map      5
Nilradical      153
Noether normalization lemma      155
Noetherian ring      153
Nonsingular      see Smooth
Normal closed subgroup      14
Nullstellensatz      155
One-parameter subgroup      60
Order of a finite group scheme      112
p-Divisible group      126
Parabolic subgroup      77
Picard group      149
Picard — Vessiot extension      77
Pointed coalgebra      72
Polynomial map      28
Prime ideal      153
Primitive element      14
Principal homogeneous space      142
Quotient map      114
Radical of G      97
Rank of a smooth group      77
Rational point      33
Reduced ring      153
Reductive group      97
Regular local ring      89
Regular representation      23
Relatively closed set      157
Represcntable functor      5
Representation      see Linear representation
Representation of a Lie algebra      96
Ring of functions on S      30
Root system      98
Ruler's theorem      75
Scheme      44
Schur's lemma      63
Semi-direct product      19
Semi-invariant element      34
Semisimple group      97
Separable algebra      47
Separable matrix      54
Sheaf      43
Sheaf in fpqc topology      117
Smooth group scheme      88
Solvable group scheme      73
Spec A      41
Split torus      56
Strictly upper triangular      62
Subcomodule      23
Symplectic group      99
Tate — Barsotti group      see p-Divisible group
topology      156
Torsor      see Principal homogeneous space
Torus      55
Triangulable group scheme      72
Twisted form      134
Unipotent group scheme      63
Unipotent matrix      62
Unipotent radical      97
Unitary group      99
Weil restriction      61
Weyl group      77
Yoneda Lemma      6
Zariski covering      117
Zariski topology on $k^n$      28
Zariski topology on Spec A      42
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