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 toms 56
Anti-equivalence 15
Antipore 8
Arf invariant 147
Artin — Schreier theory 143
Augmentation ideal 13
Automorphism group scheme 58
Base change 11
Borel subgroup 77
Cartan subgroup 77
Cartier duality 17
Center of a group scheme 27
Central simple algebra 145
CHARACTER 14
Charater group 55
Clopen set 42
Closed embedding 13
Closed set in  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
Cokereel 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  -action 48
Continuous function 157
Coseparable coalgebra 53
Crossed homomorphism 137
Dense set 157
Derivation 83
Derived group 73
Descent data 131
Diagonalizable group scheme 14
Differenfal field 77
Differential operator 99
Differentials of an algebra 84
Dimension of an algebraic G 88
Direct limit 151
Distribution (supported at e) 99
Dtployt see Split
Dual see Cartier duality
Etale finite group scheme 49 91
Etale topology 118
Euler's theorem 75
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 map 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
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 70
Kernel of a group scheme map 14
Kmll intersection theorem 154
Kolchin fixed point theorem 62
Kummer theory 143
Lie algebra 93
Lie — Kolchin triangularization theorem 74
Linear algebraic group defined over k 33
Linear representafon 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
Representable functor 5
Representation see Linear representation
Representation of a Lie algebra 96
Ring of functions on S 30
Root system 98
Scheme 44
Schur's lemma 63
Semi-direct product 19
Semi-invariant element 34
Semisimpie 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 toms 56
Strictly upper triangular 62
Subcomodule 23
Symplectic group 99
Tate — Barsotti group see p-Divisible group
Tomor see Principal homogeneous space
Toms 55
topology 156
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 coveting 117
Zariski topology on 28
Zariski topology on Spec A 42
|
|
|
О проекте