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| Ueno K., Kato G. — Algebraic Geometry 3: Further Study of Schemes (Translations of Mathematical Monographs Vol. 218) |
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| Предметный указатель |
2-torsion points 162
A-derivation 81
Abelian variety 173
Abelian variety, dual 179
Abelian variety, principally polarized 179
Albanese variety 179
Algebraic function field of one varialbe 134
Algebraic function theory 134
Algebraic scheme 9
Algebraic scheme, defined over k 9
Algebraic variety 7
Algebraic variety, affine 4
Algebraic variety, complete 10
Algebraic variety, exceptional 102
Algebraic variety, non-singular 28 89
Algebraic variety, rational 145
Algebraic variety, unirational 145
Analytic coherent sheaf 183
Analytic set 184
Analytic space 183
Analytic space, compact complex 184
Analytic space, complex 184
Argumentation 171
Associated point of a coherent sheaf 61
Associated point of a scheme 62
Bertini's theorem 52
Blowing down 67
Blowing up 67 101
Branch point 36 136
Bundle, cotangent 91
Bundle, dual 91
Bundle, normal 92
Bundle, tangent 91
Canonical form of the defining equation for an elliptic curve 158
Cartier dual 171
Chow's Lemma 74
Chow's theorem 187
Codimension 23
Coinverse 171
Commutative ring, etale over A 108
Commutative ring, smooth over A 108
Commutative ring, unramified over A 108
Complete intersection 22
Complete linear system 51
Complete linear system, base points of 51
Complete linear system, dimension of 51
Complete linear system, fixed component of 51
Complete local ring 117
Completion of an  -module  along Y 118
Completion of R with respect to I 116
Comultiplication 170
Counit 171
Covering, cyclic 57
Covering, etale 149
Covering, etale, abelian 151
Covering, etale, trivial 149
Covering, unramified 57
Curve, elliptic 32 153
Curve, elliptic, ordinary 148
Curve, elliptic, supersingular 148
Curve, hyperelliptic 33 35
Curve, ordinary 148
Curve, singular 148
Curve, supersingular 149
Degeneration of a curve 71
Degree of a divisor 41
Differential module 81
Dimension of a complete linear system 51
Dimension of X at x 59
Divisor 39 45
Divisor class group 40
Divisor, canonical 92
Divisor, Cartier 42 43
Divisor, degree of 41 125
Divisor, effective 39 45
Divisor, prime 39
Divisor, principal 40
Divisor, very ample 130
Divisor, Weil 39
Divisor, Weil, linearly equivalent 40
Element integral over a ring 15
Elliptic modular function 168
Extension, unramified at x 11
Family, universal flat 73
Field of definition 9 152
Field, perfect 13
Flat R-module 53
Formal completion of X along Y 118
Frobenius homomorphism, nilpotent 148
Function field 25
Functor, fully faithful 7
GAGA 186
Genus of a curve 126
Group scheme 153 168
Group scheme, affine 170
Group scheme, commutative 168
Group scheme, finite 171
Group scheme, finite, order of 171
Group scheme, local 172
Height of a prime ideal 14
Hilbert polynomial 78 80
Hilbert scheme 72 80
Hodge decomposition 188
Holomorphic function 120
Homomorphism, flat 54
Hurwitz formula 138
Hyperplane section 105 124
I-adic completion 116
Ideal-class group 42
Inflection point 156
Integral closure of a ring 16
Integral extension of a ring 15
Integrally closed domain 16
Integrally closed ring 16
Invariants 163
J-invariant 165
Jacobian criterion 30
Jacobian variety 175
Kaehler differential 81
| Kodaira's Vanishing Theorem 189
Koszul complex 101
Krull dimension 14
Krull's altitude theorem 23
Lefschetz principle 189
Line bundle, canonical 92
Local coordinates 98
Local ring, Cohen — Macauley 100
Local system 190
Lueroth theorem 144
Mapping, birational 50
Mapping, rational 50
Mapping, rational, domain of 50
Mittag — Leffler condition 114
Module, Cohen — Macaulay 100
Module, differential 81
Module, faithfully flat over R 53
Module, fiat over Y at x 54
Module, flat over R 53
Moduli 163
Morphism 142
Morphism of local ringed spaces 3
Morphism, Artin — Schreier 12
Morphism, birational 50 74
Morphism, etale 11 112
Morphism, flat 11 55
Morphism, formally etale 111
Morphism, formally smooth 111
Morphism, formally unramified 111
Morphism, Frobenius 142
Morphism, Frobenius, k-linear 13 143
Morphism, identity point 169
Morphism, inverse 169
Morphism, multiplication 169
Morphism, normalization 37
Morphism, purely inseparable 137
Morphism, ramified 12
Morphism, separable 135
Morphism, smooth 112
Morphism, unramified 11 112
Morphism, unramified at P 136
N-form, rational 99
N-form, regular 99
Noether's normalization theorem 18
Normal ring 16
Normalization of a ring 16
Normalization of an integral scheme 37
Normalization of SpecR 18
Oka's theorem 183
Orbit 181
P-form, rational 99
P-form, regular 99
Picard variety 179
Poincare invertible sheaf 175
Point, regular 28
Point, singular 28
Profinite completion 149
Projective limit 114
Projective line, N-pointed 68
Proper mapping theorem 75
Quotient singularity 45
Ramification index 136
Ramification point 136
Ramification, tame 136
Ramification, wild 136
Rational double point of type Ai 71
Relative dimension 24
Relative tangent sheaf 91
Relatively minimal surface 198
Residue of a rationa 1-form 141
Residue theorem 141
Resolution of singular points on a curve 134
Riemann — Roch theorem 127
Ring of p-adic integers 116
Ring, regular 29
Ring, regular local 28
Ruled surface 198
Scheme, absolutely integral 10
Scheme, absolutely irreducible 10
Scheme, algebraic 9
Scheme, algebraic, defined over k 9
Scheme, field of definition 152
Scheme, flat over Y 55
Scheme, formal 118
Scheme, formal, algebraizable 119
Scheme, geometrically integral 10
Scheme, geometrically irreducible 10
Scheme, geometrically regular 107
Scheme, Hilbert 72 80
Scheme, locally factorial 43
Scheme, normal 26
Scheme, regular 28
Scheme, regular in codimension 1 39
Sequence, M-regular 99
Sequence, M-regular, depth of 100
Sequence, regular 99
Serre duality 107
Sheaf of regular m-forms 92
Sheaf of relative differential 1-forms 88
Sheaf of relative differentials 88
Sheaf, canonical 92
Sheaf, conormal 92
Sheaf, normal 92
Simply connected 149
Spectrum, maximal 2
Stable 4-pointed curve 69
Stein factorization 121
Subgroup scheme 170
Symmetric product of degree n 175
System of parameters, local 98
System of parameters, local, with center x 98
System of parameters, regular 97
Theorem of formal functions 120
Theta functions 201
Total transform of a divisor 49
Translation 179
Transverse intersection 102
Upper semicontinuous function 76
Zariski tangent space 91
Zariski's main theorem 120
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