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Ueno K., Kato G. — Algebraic Geometry 3: Further Study of Schemes (Translations of Mathematical Monographs Vol. 218)
Ueno K., Kato G. — Algebraic Geometry 3: Further Study of Schemes (Translations of Mathematical Monographs Vol. 218)

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Название: Algebraic Geometry 3: Further Study of Schemes (Translations of Mathematical Monographs Vol. 218)

Авторы: Ueno K., Kato G.

Аннотация:

This is the third and final part of a textbook intended for a graduate course on algebraic geometry (the first two were published as volumes 185 and 197 of this series). Containing chapters 7 through 9, as well as the solutions to exercises, the author covers the fundamental properties of scheme theory, algebraic curves and Jacobian varieties, analytic geometry, and Kodaira's vanishing theorem. Translated from the Japanese Daisu kika.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 222

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\mathcal{O}_X$-module $\mathcal{F}$ 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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