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Bump D. — Algebraic Geometry and the Theory of Curves
Bump D. — Algebraic Geometry and the Theory of Curves

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Название: Algebraic Geometry and the Theory of Curves

Автор: Bump D.

Аннотация:

A text for a one-year course at the graduate level, for students with substantial background in algebra. Eight chapters contain material applicable to varieties of every dimension, and six chapters contain material which is particular to the theory of curves. Material considers irreducible varieties over an algebraically closed field, except in one chapter, which works over a finite field. Coverage includes the extension theorem, maps of affine varieties, complete nonsingular curves, and the Riemann-Roch theory. Intersection theory is not covered. Includes chapter exercises. The author teaches mathematics at Stanford University.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 250

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian variety      183
Abstract function field      19 140
Additivity of length      45
Adele      164
Adic topology      126
Affine algebra      15 16
Affine open set      82
Algebra      106
Algebraic group      183
Algebraic Nullstellensatz      8
Algebraic set      1
Ascending chain condition      5
Birational equivalence      19 88
Birational map      19 88
Birational morphism      76
Biregular      14
Blowing up      92 93
Boolean algebra      77
Canonical class      168
Canonical dissection      137
Canonical divisor      168
Cartier operator      144
Cartier operators      138 143
Cauchy sequence      125
Chain of irreducible spaces      29
Chain of prime ideals      29
Chart      79 84
Chinese remainder theorem      107
Cocycle relation      199
Codimension      23
Cofinal      80
Collinear points      180
Combinatorial dimension      29
Compactification      78
complete      87
Complete field      127
Complete linear system      163
Complete nonsingular curve      97
Complete topological group      125
Complete variety      163
Completion      125 126 129
Complex multiplication      184 210
Component of a Noetherian space      4
Composition factors      44
Composition series      44
Compositum of fields      132
Constructible set      77
Continuous derivation      145
Coordinate ring      13
Coordinate ring, contravariance of      14
Coprime ideals      107 120
Coproduct      37
Curve      23 86
Curve, complete nonsingular      97
Decomposition field      115
Decomposition group      115
Dedekind domain      104
Dedekind domain, unique factorization in      120
Defined over a field      198
Degree of a morphism      103
Derivation      40 138 186
Derivation, continuous      145
Descending chain condition      3
Desingularization      71 92
Differential, Kahler      138
Differentiate      39
DIMENSION      23 49 161
Dimension, combinatorial      29
Dimension, Krull      29
Direct limit      80
Directed family      80
Directed set      80
Discrete valuation      57
Discrete valuation ring      57
Divisor      159
Divisor class group      201
Divisor of a differential      168
Divisor of a function      159
Divisor of poles      160
Divisor of zeros      160
Divisor, effective      160
Divisor, positive      160
Divisor, prime      197
Dominant morphism      21 95
Dominant rational map      19 21 61 88
Dual numbers      65
Effective divisor      160
Elliptic curve      175
Equivalence of categories      22
Euler product      195
Extending a valuation      110 130
Extension of scalars      106 121
Extension theorem      7
External direct sum      189
Fiber of a dominant map      61
Fiber product      71
Field of definition, minimal      199
Field of formal power series      127
Finite morphism      38 62
Flat module      122
Fractional ideal      121
Free module      106 122
Frobenius endomorphism      207
Frobenius map      20 161
Function field      16 17 19 140 161
Function field of dimension one      97
Fundamental system of neighborhoods of the identity      125
Galois morphism      103
Genus      167
Going down theorem      25 26 27 29
Going up theorem      11 25 26
Graded modules      45
Graded ring      45 46
Graph of a morphism      61
Hausdorff space      3
Height of a prime      32
Hilbert basis theorem      1 5
Hilbert series      46
Hilbert's "Theorem 90"      199
Hilbert's Nullstellensatz      1 2
Hilbert's ramification groups      135
Holomorphic function      18
Holomorphic functions      16
Homogeneous coordinates      93
Homogeneous element      45 46
Homogeneous ideal      53
Homogeneous part      45 46
Homomorphism of abelian varieties      184
Hyperplane      90
Hypersurface      31
Ideal, radical      1
Inertia field      115
Inertia group      115
Integral closure      10
Integral ideal      121
Integral over a ring      10
Integral over an ideal      26
Integrally closed      27
Integrally closed ring      10
Intersection multiplicity      163
Irreducible      3
Irreducible algebraic set      5
Irreducible ideal      52
Isogeny      185
Isomorphism      20
Isomorphism of composita      132
Kaehler differential      138
Krull dimension      29 32 49
Krull dimension theorem      52
Length      29 44 45
Lie above      25 99
Lie algebra      187
Line in $P^2$      180
Linear subspace of $P^n$      90
Linear system      163
Linear system cut out by hyperplanes      163
Linearly disjoint extensions      141
Linearly equivalent divisors      160
Local parameter      143
Local ring      7
Local uniformizing parameter      143
localization      17
Locally closed set      77
MacLane's criterion      141
Meromorphic function      18
Meromorphic functions      16
Minimal field of definition      199
Module of fractions      17
Morphism      14 86
Morphism of presheaves      79
Morphism of prevarieties      81 83
Morphism of ringed spaces      81
Morphism of sheaves      79
Morphism of sheaves of rings      81
Morphism, dominant      21
Morphism, Galois      103
Morphism, purely inseparable      103
Morphism, separable      103
Multiplicative set      17
Noetherian graded algebra      45
Noetherian ring      5
Noetherian space      3
Nondegenerate bilinear form      71
Nonsingular point      43 53 88
Nonsingular variety      53 88
Norm      71 196
Normal point      74
Normal variety      73
Normalization      71 73 89
Nullstellensatz      1 2 8
Nullstellensatz, algebraic      8
Nullstellensatz, strong      2
Nullstellensatz, weak      1 9
Numerical polynomial      60
One point compactification      78
Opposite category      15
Order of vanishing      58
Perfect field      68
Points of ramification      104
Polarization      206
Positive definite quadratic form      206
Positive divisor      160
Presheaf      79
Prevariety      82
Primary ideal      48 59
Prime divisor      197 199
Principal open set      20
PRODUCT      23
Projective space      79
Projective variety      86
Proper mapping      70 78
Proper morphism      71
Purely inseparable morphism      103
Quadratic form      206
Quadric surface      60
Quasi-affine prevariety      84
Quasi-projective variety      86
Radical      5
Radical ideal      1 6
Radical of an ideal      1
Ramification groups      135
Ramification index      104 108 111
Ramified prime      108
Rank of a free module      106 122
Rational divisor      199
Rational function field      92
Rational map      18 88
Rational map, dominant      19 21 88
Rational point      199
Rational surface      92
Reduced ring      16
refinement      29
Regular derivation      186
Regular function      17 18 19 83
Regular local ring      53
Regular map      14
Relation      80
Repartition      164
Residue class degree      108
Resolution of singularities      71 92
Restriction map      79
Riemann hypothesis      195
Ring      1 7
Ring of formal power series      127
Ring of fractions      17
Ringed space      81
Saturated chain      29
Separable extension      141
Separable morphism      103
Separably generated extension      68 141
Separated prevariety      86
Sheaf      22 80
Sheaf axiom      80
Simple module      44
Singular point      43 53 70 88
Singularity      53
Smooth point      43 53 88
Smooth variety      53 88
Stalk of a sheaf      81
Strong Nullstellensatz      2
Structure map      106
Structure sheaf      81
Support of a divisor      159
surface      23 86
Tame ramification      118 170
Tangent bundle      65
Tangent space      40
Torsion element      107
Torsion module      107
Torsion-free module      107
Totally ramified prime      108
Trace      71
Trace bilinear form      71
Trace of a differential      152
Transcendence basis      23
Transcendence degree      23
Translation      177
Transpose of a morphism      192
Underlying mapping      81
Unique factorization in Dedekind domains      120
Universal module of derivations      138
Universal property      37
Valuation ring      7
Valuation, discrete      57
Valuative criterion for completeness      89
Variety      3 16 79 86
Weak Nullstellensatz      1 9
Weierstrass form      178
Weil divisor      162
Wild ramification      118 170
Zariski closed set      14
Zariski tangent space      40
Zariski topology      2 3 14 20 79
Zariski's main theorem      77
Zeta function      195 198
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