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