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Bochnak J., Coste M., Roy M-F. — Real algebraic geometry
Bochnak J., Coste M., Roy M-F. — Real algebraic geometry



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Название: Real algebraic geometry

Авторы: Bochnak J., Coste M., Roy M-F.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 220

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Alexandrov compactification, algebraic      77
Alexandrov compactification, semi-algebraic      42
Algebraic homology      272 318
Algebraic model      273 317
Algebraic power series      165
Algebraic projective-set      70
Algebraic real-variety      64
Algebraic set      23
Algebraic, affine variety      3 72 305
Approximation, algebraic      318
Archimedean      7
Artin — Lang theorem      84
Artin — Mazur theorem      173 376
Artin's approximation theorem      171
Basic, closed semi-algebraic set      46 111 259 285
Basic, generically      107
Basic, open semi-algebraic set      46 122
Bertini's theorem, semi-algebraic      236
Betti numbers      266 276 284
Bezout's theorem      281 287
Bilinear space      384
Birationnally equivalent      75
Biregular isomorphism      63
Blowing down      77
Blowing up      78 319
Borel — Moore homology      278 294
Broedcker — Scheiderer theorem      122 405
Cartan's umbrella      60 105 237
Cellular decomposition, semi-algebraic      213
Central points      158 250
Centre of a place      249
Chern class      327 362
Cobordism      377
Cohomology      291
Cohomology, algebraic      273
Cohomotopy group      361
Complete semi-algebraic set      74
Cone of a field      8
Cone of a ring      86
Cone, positive, of an ordered field      8
Cone, prime      88
Cone, proper      8 86
Conic, local structure      225 295
Connected sum      82
Connected, semi-algebraically      34
Connected, semi-algebraically - components      34 75 285 392
Connected, semi-algebraically path      42
Constructible subset      137
Constructible topology      137
Convex ,P- ideal      87
Convex envelope      249
Convex, subring      247
Critical point      235
Critical value      235
Curve selection lemma      38
Curve selection lemma, Nash      167 240
Curve, dividing      288 331
Curve, M-      288
Descartes's law of signs      14
Desingularization, topological      380
Diffeotopy      318 373
Dimension of a constructible subset      155
Dimension of a prime cone      157
Dimension of a quadratic form      114
Dimension of a ring      50
Dimension of a semi-algebraic set      50
Dimension of an ideal      65
Dimension, local      53
Distance to a semi-algebraic set      29
Division theorem for Nash functions      169
Division theorem formal      168
Divisor class group      306
Efroymson's extension theorem      200
Equivalence of quadratic forms      114
Etale mapping      162
Euler — Poincare characteristic      267
Euler — Poincare, local characteristic      267
Extension of a semi-algebraic mapping      101 151
Extension of a semi-algebraic set      98 150
Face of a simplex      216
Factoriality      169 306 308 319 327 337
Family of Nash functions      202
Family, semi-algebraic, of mapping      149
Family, semi-algebraic, of sets      149
Fan      257
Fan, trivial      257
Filter      137
Filter, prime      138
Finiteness theorem      46 131
FORM      340
Form, nonsingular bilinear      346
Form, normed bilinear      340
Formula, first-order      28
Formula, quantifier-free      28 99
Fundamental class      271 278
Generization      140
Grassmannian      71 272 300 352
Grothendieck group      310
Half-branches      232 254
Half-branches at infinity      234
Half-branches of a Nash curve      234
Hardt's theorem      221
Harnack's theorem      286
Henselian local ring      185
Henselization      186
Hilbert's problem, 16-th      285
Hilbert's problem, 17-th      103
Homogeneous coordinates      70
Homology, algebraic      272 318
Homology, Borel — Moore      278 294
Homology, local      295
Homology, relative      293
Homology, totally algebraic      272
Homotopy      291 334 361
Hopf form      340
Hurwitz — Radon function      341
Hyperbolic space      385
Ideal, fractional      306
Ideal, P-convex      87
Ideal, P-radical      87
Ideal, real      84
Implicit function theorem, semi-algebraic      56
Integral closure      75 163
Invertible modules      306
Irreducible algebraic set      50
Irreducible Nash set      180
Isolated singularities      380
Isometry between bilinear spaces      384
Knot      375
Line bundle, algebraic      306 327
Local-etale      184
Lojasiewicz's inequality      44
M-curves      288
Mapping, Nash      57
Mapping, polynomial      62
Mapping, regular      62
Mapping, semi-algebraic      28 54
Model, algebraic      273 317
Morphism, algebraic, of vector bundles      298
Nash diffeomorphism      57
Nash equivalence      181
Nash function      48 55
Nash mapping      57
Nash submanifold      57 68 227
Nash subset      178
Nash tubular neighbourhood      199
Nash wing      239
Nash's theorem      377
Nest      289
Nonsingular in dimension d      67
Nonsingular point      66
Nonsingular variety      67
Normalization      75
Nullstelleusatz for Nash functions      179
Nullstelleusatz, central      159
Nullstelleusatz, real      84
Ordered field      7
Ordering of a field      7
Ordering, compatible with a place      247
Orthogonal sum of bilinear spaces      384
Orthogonal sum of quadratic forms      115
Oval      286
Oval, depth of an      289
Oval, even      290
Oval, odd      290
Pfister form      117 158
Picard group      306
Place      245
Place, centre of a      249
Place, finite on a ring      249
Place, real      247
Poincare duality      273 313
Positivstellensatz      92
Positivstellensatz for Nash functions      178
Positivstellensatz, formal      91
Preparation theorem for Nash functions      169
Preparation theorem, formal      168
Projective modules      302 309 334 336 383
Projective space      70
Pseudo-line      286
Puiseux series      11 16 148
Pythagoras number      114 128 129
Quadratic form, anisotropic      115
Quadratic form, isotropic      115
Quadratic form, multiplicative      118
Quadratic form, nondegenerate      115 124
Quadratic form, representing an element      115
Quantifier elimination      99
Quasi-monic      38 207
Ramification index      252
Rank of a projective module      384
Rank of a vector bundle      298
Real algebraic numbers      11
Real closed field      9
Real closure      14
Real field      9
Real ideal      84
Real Nullstellensatz      84
Real place      247
Real principal ideal      94
Real radical      85
Real spectrum      134
Real valuation ring      247
Regular function      62
Regular germs of- functions      65
Regular local ring      66
Regular mapping      62 64
Regular system of parameters      66 246
Residual degree      252
Sard's theorem, semi-algebraic      235
Semi-algebraic cellular decomposition      213
Semi-algebraic family of mappings      149
Semi-algebraic family of sets      149
Semi-algebraic fibre of a family      149
Semi-algebraic function      28 65
Semi-algebraic generically equal sets      107
Semi-algebraic implicit function theorem      56
Semi-algebraic mapping      28
Semi-algebraic set      24
Semi-algebraic subset of a real algebraic variety      65
Semi-algebraic Tietze — Urysohn theorem      45
Semi-algebraic topological type      230
Semi-algebraic trivialization      221
Semi-algebraic, closed and bounded, set      35
Semi-algebraic, complete, set      74
Semi-algebraically connected      34
Semi-algebraically connected components      34 75 154 392
Semi-algebraically homotopic      291
Semi-algebraically path connected      42
Semi-algebraically, trivial      230
Separation theorem      49 394
Serf-intersection number      329 360
Sheaf of continuous semi-algebraic functions      146
Sheaf of Nash functions      192
Sheaf of regular functions      63 64
Sheaf, locally free algebraic      300
Signature homomorphism      386
simplex      216
Simplex, open      217
Simplicial complex, finite      217
Slicing      33
Specialization      140
Specialization chain      155
Stable equivalence classes      309 310
Stable isomorphism classes      383
Stable under derivation      37
Stereographic projection      76 364
Stiefel — Whitney class      274 304 312 321 353
Stone space      137
Stone — Weierstrass theorem      193 308 321
Stratification, induced by a stratifying family      210
Stratification, Nash      212
Stratification, satisfying Whitney's conditions      242
Stratifying family of polynomials      207
Stratum      210
Stratum of a Nash stratification      212
Stratum, contiguous strata      269
Sturm sequence      12
Sturm's theorem      13
Submanifold, Nash      57 227
Substitution theorem for Nash functions      176
Sums of squares      8 103 111
Support      88
Suspension of a form      367
Sylvester's theorem      12
Tangent space to a Nash submanifold      197
Tangent space, Zariski      65
Tarski — Seidenberg principle      17 26 28 98
Tensor product of bilinear spaces      384
Tensor product of quadratic forms      115
Tensor product of vector bundles      299
Thom's lemma      37
Tietze — Urysohn theorem, semi-algebraic      45
Tilde operation      143
Tognoli's theorem      378
Topological type, semi-algebraic      230
Topology, constructible      137
Topology, euclidean      26 65
Topology, spectral      134
Topology, Zariski      26 64
Transfer principle      99
Triangulation      217
Triangulation of semi-algebraic functions      227
Trivial, algebraically, vector bundle      298
Tsen — Lang theorem      120
Tubular neigbourhood, Nash      199
Ultrafilter      137
Uniformizing parameter      246
Valuation of a field      245
Valuation, discrete, ring      246
Valuation, real, ring      247
Valuation, ring      245
Value group      246
Variety, affine algebraic      63 72 305
Variety, real algebraic      64
Vector bundle, algebraic      302 385
Vector bundle, algebraic section of a      298
Vector bundle, induced      298
Vector bundle, Nash      335
Vector bundle, pre-algebraic      297
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