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Weil A. — Foundations of Algebraic Geometry
Weil A. — Foundations of Algebraic Geometry

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Название: Foundations of Algebraic Geometry

Автор: Weil A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1946

Количество страниц: 288

Добавлена в каталог: 28.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abstract field      I 1 1
Abstract variety      VII 1 167
Algebraic closure      I 1 1
Algebraic closure in      I 1 1
Algebraic over (a field), bunch of varieties      IV 4 85
Algebraic over (a field), normally      IV 4 86
Algebraic over (a field), separably      I 4 8
Algebraic over (a field), set of generalized quantities      II 1 28
Algebraic over (a field), set of quantities      1 2 2
Algebraic over (a field), variety      IV 2 76 (a.c.) 2 177
Algebraic projection (of cycles)      VII 6 208
Algebraically closed in (a field)      I 1 1
Ambient Space      IV 1 69
Ambient Variety      VII 2 174
Attached to, linear variety, a variety      IV 6 98
Attached to, point-set, a bunch of varieties      IV 4 84
Attached to, point-set, a variety      IV 1 69 (a.c.) 2 178
Birational correspondence      IV 7 109 (a.c.) 4 188
Birationally equivalent      IV 7 109
Biregular      IV 7 110 (a.c.) 4 189
Bunch of varieties      IV 4 84 (a.c.) 2 178
Bunch of varieties algebraic (normally algebraic) over a field      IV 4 85—86
Bunch of varieties, empty      IV 4 84
Bunch of varieties, point of (in) a      IV 4 84
Bunch of varieties, point-set attached to a      IV 4 84
Coefficient (of a Variety in a cycle)      VII 6 197
Coherent (birational correspondences)      VII 1 166
Compatible (specialization, with)      II 2 30
complete      VII 1 168
Complete over (a Point, a Variety)      VII 4 185—186
Complete set of conjugates      I 4 9
Complete set of intersections      V 1 119
Component of a bunch (of an intersection)      IV 4 85 (a.c.) 2 178
Component of a cycle      VII 6 197
Component, proper, of an intersection      V 1 117 VI 1 146 (a.c.) 5 189
Cone      App. I 263
Conjugate of a bunch of varieties      IV 4 86
Conjugate of a set of quantities      1 4 9
Conjugate of a variety      IV 2 76 (a.c.) 2 177
Conjugate, complete set of      I 4 9
Constant      VIII 1 216
Contain (to), contained in, (bunches of varieties)      IV 4 84
Contain (to), contained in, (varieties)      IV 1 69 (a.c.) 1 170
Contain (to), contained in, cycle contained in a Variety      VII 6 212
Coordinate of a point      IV 1 68
Coordinate of a Point of D, VIII      1 215—216
Correspondence (birational)      IV 7 109 (a.c.) 4 188
Corresponding, generic points (by a birational correspondence)      IV 7 110
Corresponding, generic points (by a set of coherent birational correspondences)      VII 1 166
Corresponding, regularly (points, varieties, by a birational correspondence)      IV 7 110 (a.c.) 4 189
CYCLE      VII 6 197
Cycle, component of      VII 6 197
Cycle, degree of      VII 6 198—199
Cycle, expression (reduced expression) for a cycle      VII 6 197
Cycle, generic Point of a prime rational, over a field      VII 6 200
Cycle, positive      VII 6 198
Cycle, rational, prime rational (over a field)      VII 6 198
Cycle, specialization of (of dimension 0)      VII 6 205
def (as symbol)      IV 1 72
Defined, bunch of varieties, over (a field)      IV 4 85
Defined, function, along (a Variety)      VIII 1 218
Defined, function, over (a field) by (a relation)      VIII 1 216
Defined, variety, by (an ideal, a set of equations)      IV 1 70
Defined, variety, by (representatives, frontiers and birational correspondences)      VII 1 167
Defined, variety, over (a field)      IV 1 68 (a.c.) 1 167
Defining, (ideal, set of equations), (a variety)      IV 1 70
Definition      cf. “Field of definition”
deg (as symbol)      VII 6 198 and 266
Degree (of a cycle in a projective space)      App. I 266
Degree (of a cycle of dimension 0)      VII 6 198
Degree (of an algebraic extension)      I 2 2
Degree, separable (inseparable) factor of the, (of an algebraic extension)      I 4 9
Derivation      I 5 11
Determined, ideal, by (a set of quantities) over (a field)      I 3 6
Diagonal      VI 1 143 (a.c.) 4 189
dim (as a symbol)      I 2 2; 1 27; 1 72 (a.c.) 2 173
Dimension of (a cycle)      VII 6 197
Dimension of (a set of generalized quantities) over (a field)      II 1 27
Dimension of (a variety)      IV 1 72 (a.c.) 2 173
Dimension of (an extension, a set of quantities) over (a field)      I 2 2
Disjoint, linearly      I 2 4
Divisor      VII 6 198
Divisor of (a function)      VIII 2 224
Empty (bunch of varieties)      IV 4 84
Equation, generic set of linear      IV 5 96
Equation, irreducible (for a set of quantities over a field)      I 3 8
Equation, minimal set of linear (for a linear variety)      IV 5 93
Equation, set of (for a variety, or defining a variety)      IV 1 70
Equivalent (birationally)      IV 7 109
Expression, reduced (for a bunch of varieties)      IV 4 85
Expression, reduced, (for a cycle)      VII 6 197
Extend (to) a specialization      II 2 30
Extension (of a field)      I 1 2
Extension (of a field), algebraic      I 2 2
Extension (of a field), degree of an (algebraic)      cf. “Degree”
Extension (of a field), dimension of an      I 2 2
Extension (of a field), purely inseparable      I 4 8
Extension (of a field), purely transcendental      I 2 4
Extension (of a field), regular      I 7 18
Extension (of a field), separable (separably algebraic)      I 4 8
Extension (of a field), separably generated      I 5 14
Extension (of a specialization)      II 2 30
Factor (of a product of varieties)      IV 3 79 (a.c.) 3 183
Factor (of a product of varieties), separable (inseparable), of the degree (of an algebraic extension)      I 4 9
Field      I 1 1
Field generated by (a set of quantities) over (a field)      I 1 2
Field of definition, (for a function)      VIII 1 216
Field of definition, (for a variety)      IV 1 68 (a.c.) 1 167
Field of definition, smallest (for a variety)      IV 1 72
Field, abstract      I 1 1
Field, independent, free      I 2 3
Field, prime      I 1 1
Finite over (a specialization)      II 5 41
Finite, (quantity), at (a point)      App. II 268
Finite, (set of generalized quantities)      II I 27
Finite, (variety), over (a point)      IV 7 106
Free (field, extension)      I 2 3
Frontier      VII 1 166
Full set of representatives      VII 1 168
Function      VIII 1 216
Function defined along (a Variety), induced on (a Variety) by (a function)      VIII 1 218
Function defined over (a field) by (a relation)      VIII 1 216
Function, constant, constant generalized      VIII 1 216
Function, divisor of a      VIII 2 224
Function, field of definition for a      VIII 1 216
Function, generalized      VIII 1 217
Function, graph of a      VIII 1 218
Generalized function      VIII 1 217
Generalized, quantity      II 1 26
Generated, (extension), by (a set of quanlities) over (a field)      I 1 2
Generated, separably      1 5 14
Generic Point of (a prime rational cycle) over (a field)      VII 6 200
Generic point of (a variety) over (a field)      IV 1 68 (a.c.) 2 173
Generic set of linear equations over (a field)      IV 5 96
Generic, (specialization)      II 1 27
Generic, corresponding, points by (a birational correspondence)      IV 7 110
Generic, corresponding, points by (a set of coherent birational correspondences)      VII 1 166
Graph (of a function)      VIII 1 218
Homogeneous ideal      App. I 264
Homogeneous, set of, coordinates      App. I 263
Homogeneous, set of, equations, App      I 265
i (as a symbol)      VI 1 148 (a.c.) 5 189
Ideal defining (a variety over a field)      IV 1 70
Ideal, determined by (a set of quantities) over (a field)      I 3 6
Independent, (extensions, sets of quantities)      I 2 3
Independent, (variables)      I 2 4
Induce (to), induced by (function)      VIII 1 218
Infinite      II 1 27
Inseparability, (for a variety)      V 1 123 (a.c.) 2 177
Inseparability, order of (for an extension)      I 8 22
Inseparable      I 4 8
Inseparable, factor of the degree      I 4 9
Inseparable, purely, over (a field)      I 4 8
Integral over (a ring)      III 3 52
Integrally closed      App. II 268
Intersect, to, properly      VII 6 201
Intersection, (of varieties, of bunches of varieties)      IV 4 88—89 (a.c.) 2 178
Intersection, complete set of      V 1 119
Intersection, point of      V 1 117
Intersection, proper component of an      V 1 117 VI 1 146 (a.c.) 5 189
Intersection-multiplicity      V 1 121 V 2 130 VI 1 148 (a.c.) 5 189
Intersection-product      VII 6 202
Irreducible equation (for a set of quantities over a field)      I 3 8
Isolated specialization      II 3 32
j (as a symbol)      V 1 121 V 2 130
Lie, to, properly over (a Point, a Variety)      VII 4 186
Linear equations, generic set of, over (a field)      IV 5 96
Linear equations, minimal set of (for a linear variety)      IV 5 93
Linear equations, set of      IV 5 90
Linear forms, unlformizing set of      IV 6 100—102
Linear variety      IV 5 90
Linear variety attached to (a variety) at (a point)      IV 6 98
Linear variety, parallel      IV 5 95
Linear variety, tangent, to (a variety) at (a point)      IV 6 99
Linear variety, transversal      IV 5 95
Linearly disjoint      I 2 4
Locus of (a point) over (a field)      IV 1 68 (a.c.) 2 174
Maximal multiple subvarlety      IV 6 99 (a.c.) 2 179
Maximal variety (in a bunch)      IV 4 85
Maximal variety, belonging to (a point-set)      IV 4 84 (a.c.) 2 178
Minimal set of linear equations      IV 5 93
Multiple subvarlety      IV 6 99. 2 179
Multiple, maximal, subvariety      IV 6 99 (a.c.) 2 179
Multiple, point      IV 6 99 (a.c.) 2 179
Multiplicity (of a component of an intersection)      cf. “Intersection-multiplicity”
Multiplicity (of a specialization)      III 4 62
normal      App. II 277
Normal, relatively      App. II 277
Normalization      App. II 273
Normally algebraic      IV 4 86
Operations (on cycles), algebraic projection      VII 6 208
Operations (on cycles), intersection-product      VII 6 202
Operations (on cycles), operation X      VII 6 203
Order of inseparability      cf. “Inseparability”
Over (a field)      I 1 1 etc
Over (a specialization, with reference to a field)      II 2 30
Over, finite      cf. “Finite”
Over, proper specialization (a specialization)      cf. “Proper”
Over, to lie properly      cf. “Properly”
p (as symbol for the characteristic)      I 1 1
p (as symbol for the characteristic), $p^{m}$      1 4 8
Parallel (linear varieties)      IV 5 95
Partial product      IV 3 79
Point      IV 1 68 (a.c.) 2 173
Point of (a bunch of varieties), in (a bunch of varieties)      IV 4 84—85
Point of (a variety), on (a variety)      ill (a variety) IV 1 69 (a.c.) 2 173
Point, generic      cf. “Generic”
Point, locus of a      cf. “Locus”
Point, multiple      IV 6 99 (a.c.) 2 179
Point, regularly corresponding      cf. “Regularly”
Point, set of      IV 1 68
Point, simple      IV 6 99 (a.c.) 2 179
Point-set      IV 1 68 (a.c.) 2 178
Positive cycle      VII 6 198
pr (as a symbol)      VII 6 208
Prime rational cycle over (a field)      VII 6 199
Prime, field      I 1 1
Product, product-variety      IV 3 79 (a.c.) 3 181
Product, product-variety, factors of a      IV 3 79 (a.c.) 3 183
Product, product-variety, partial (of a product)      IV 3 79
Projection      IV 3 80—81 (a.c.) VII 3 184
Projection from (a variety) to (a variety)      IV 7 105 (a.c.) 4 185
Projection, algebraic (of a cycle)      VII 6 208
Projection, regular, along (a variety)      IV 7 108 (a.c.) 4 187
Projection, regular, at (a point)      IV 7 108 (a.c.) 4 187
Projective space      App. I 262
Projective straight line      VIII 1 215
Proper component (of an intersection)      V 1 117 VI 1 146 (a.c.) 5 189
Proper, specialization      III 4 62
Properly, to intersect      VII 6 201
Properly, to lie, over (a Point, a Variety)      VII 4 186
Pseudopoint      IV 1 68 (a.c.) 2 174
Purely transcendental (extension)      I 2 4
Purely, inseparable      I 4 8
quantities      I 1 1
Quantities, generalized, set of generalized      II 1 26
Quantities, set of      I 1 1
Rational (cycle) over (a field)      VII 6 198
Rational (cycle) over (a field), prime, (cycle) over (a field)      VII 6 199
Reciprocation      II 1 26
Reduced expression (for a bunch of varieties)      IV 4 85
Reduced expression (for a cycle)      VII 6 197
Reduced, (variety) to (a point)      IV 1 69 (a.c.) 2 173
Reference, with, to (a field)      I 1 1 etc
Regular over (a field), extension of (a field)      I 7 18
Regular projection      IV 7 107 (a.c.) 4 187
Regular projection along (a variety)      IV 7 108 (a.c.) 4 187
Regular projection at (a point)      IV 7 108 (a.c.) 4 187
Regularly corresponding, (points)      IV 7 110 (a.c.) 4 189
Regularly corresponding, (varieties)      IV 7 110 (a.c.) 4 189
Representation      VII 2 173 VII 3 184
Representative (of a Point)      VII 2 173
Representative (of a specialization of a set of corresponding generic points of the representatives of a Variety)      VII 1 168
Representative (of a Subvariety, in a representative of the ambient Variety)      VII 1 171
Representative (of a Variety)      VII 1 167
Representative, full set of, attached to (a Variety)      VII 1 168
Represented (simultaneously)      VII 2 172 VII 3 184
Separable      I 4 8
Separable factor of the degree      1 4 9
Separably generaled (extension)      I 5 14
Separably, algebraic      I 4 8
Set of equations, of linear equations      cf. “Equations”
Set of generalized quantities      II 1 26
Set of points, of points and pseudopoints      IV 1 68
Set of points, of points and pseudopoints (for “point-set”)      cf. “Point-set”
Set of quantities      I 1 1
Set, complete, of conjugates      I 4 9
Set, complete, of intersections      V 1 119
Set, full, of representatives      cf. “Representatives”
Set, uniforniizmg, of linear forms      cf. “Uniformizing”
Simple, (point)      IV 6 99 (a.c.) 2 179
Simple, (subvariety)      IV 6 99 (a.c.) 2 179
Simultaneously represented      VII 2 172 VII 3 184
Smallest field of definition for (a variety)      IV 1 72
Space, n-space      IV 1 69
Space, n-space, ambient      IV 1 69
Space, n-space, product-space      IV 3 80
Specialization of (a cycle of dimension 0)      VII 6 205
Specialization of (a Point) over (a field), generic, of (a Point) over (a field)      VII 2 175—176
Specialization of (a set of generalized quantities) over (a specialization) with reference to (a field)      II 2 30
Specialization of a set of linear equations      IV 5 95
Specialization, (of a set of generalizedquantities, over a field)      II 1 27
Specialization, extension of a, to extend a      II 2 30
Specialization, finite (of a set of quantities)      II 1 26
Specialization, finite (set of quantities) over a      II 5 41
Specialization, generic      II 1 27
Specialization, isolated      II 3 32
Specialization, multiplicity of a      III 4 62
Specialization, proper      III 4 62
Specialization-ring      II 4 36
Specialization-ring of a point, of a subvariety      IV 2 77 (a.c.) 2 176
Subvariety      IV 1 09 (a.c.) 1 170
Subvariety, simple, multiple, maximal multiple      IV 6 99 (a.c.) 2 179
Subvariety, specialization-ring of a      IV 2 77 (a.c.) 2 176
Tangent linear variety      IV 6 99
Transversal, (linear varieties)      IV 5 95
Transversal, (varieties)      VI 2 152 (a.c.) 5 190
Uniformizing set of linear forms, along (a subvariety)      IV 6 102
Uniformizing set of linear forms, at (apoint)      IV 6 100
Union (of varieties, of bunches of varieties)      IV 4 84 (a.c.) 2 178
1 2
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