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| Levine M., Morel F. — Algebraic Cobordism |
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| Предметный указатель |
 as oriented Borel — Moore functor 27
as oriented Borel — Moore homology theory 145
, formal group law 28
 and algebraic cobordism 6 115 110
as oriented cohomology 5
formal group law 5
universal property 6 114
Additive fund or 2
Admissible subcategory 1
Admissible subcategory, l.c.i. closed 142
Algebraic cobordism VII 7
Algebraic cobordism and 6 140 216
Algebraic cobordism and complex cobordism 8 13
Algebraic cobordism and MGL 14
Algebraic cobordism and the Chow ring 12 136 139 140 216
Algebraic cobordism and the Lazard ring 7 119
Algebraic cobordism as oriented Borel — Moore homology theory 215 221
Algebraic cobordism as oriented cohomology theory 215 221
Algebraic cobordism in degree 0 47
Algebraic cobordism, birational invariance 121
Algebraic cobordism, computations in low degree 139 140
Algebraic cobordism, definition 38
Algebraic cobordism, degree formula 11 129 230 231
Algebraic cobordism, extended 81
Algebraic cobordism, generalized degree formula 10 216 217 230
Algebraic cobordism, higher degree formula 131 231
Algebraic cobordism, homotopy property 76
Algebraic cobordism, localization property 7
Algebraic cobordism, made additive 103
Algebraic cobordism, made multiplicative 115 216
Algebraic cobordism, projective bundle formula 79
Algebraic cobordism, refined 160 165
Algebraic cobordism, topological Miration 139
Algebraic cobordism, universality 7 92 215 222
Algebraic pre-cobordism 37
Axiom, (BM1) 144
Axiom, (BM2) 144
Axiom, (BM3) 144
Axiom, (CD') 145
Axiom, (CD) 145 156
Axiom, (Dim) 26 33 36 91
Axiom, (EH) 2 91 145
Axiom, (FGL) 27 91
Axiom, (Loc') 85
Axiom, (Loc) 84 91 94
Axiom, (Nilp) 27 91
Axiom, (PB) 2 91 144
Axiom, (Sect) 26 29 37
Axiom, (Triv) 84
Blow-up formula 43 109
Cellular decomposition property 145
Chern character 6
Chern character operator 110
Chern class operator 19 22 35
Chern class operator for vector bundles 93
Chern class operator, refined 164
Chern class operator, Whitney product formula 95
Chern classes 3
Chern classes and Chern class operators 94
Chern classes in an oriented cohomology theory 94
Chow groups and algebraic cobordism 216
Chow groups as oriented Borel-Moore functor 27
Chow groups as oriented Borel-Moore homology theory 145
Chow groups, formal group law 27
Chow groups, universal property 216
Chow ring and algebraic cobordism 12 136 139 216
Chow ring as oriented cohomology 5
Chow ring, universal property 6
Cobordism cycle 20
Cobordism cycle, Chern class operator 22
Cobordism cycle, external product 23
Cobordism cycle, pull-back 22
Cobordism cycle, push-forward 21
Complex cobordism VII 7—9 12 117
Conner — Floyd theorem 6 14 115 216
Conner — Floyd, Chern class endomorphism 99 225—227
Deformation diagram 56 193 205 219 221 222
Deformation diagram, extended 202
Deformation to the normal bundle 41 168
Deformation to the normal cone 56
Degree formula 11 122
Degree formula for algebraic cobordism 129 134 230 231
Degree formula, generalized 125 127—129 216 217
Degree homomorphism 9
Distinguished lifting 184 IV.
Distinguished lifting of divisor classes 188
Distinguished lifting, uniqueness 187
Divisor class 53 58 218
Divisor class, refined 164 167
Elementary cobordism 38
Excess intersection formula 209 211
Extended homotopy property 3 85
Extended homotopy property as axiom 85 91 145
Extended homotopy property in algebraic cobordism 81
External product 144
Face 53
Formal group law 4 26 44
Formal group law of  27
Formal group law of 28
Formal group law of 5
Formal group law of an oriented Borel — Moore functor of geometric type 26
Formal group law of an oriented theory 4
Formal group law of the Chow ring 5
Formal group law, additive 5
Formal group law, geometric construction 87
Formal group law, logarithm 103
Formal group law, multiplicative 5
Formal group law, periodic 92
Formal group law, universal VII
Fulton, William VIII X 5 28 41 73 111 113 145 159 160 201 210
Fundamental class 146
General position 162 165
General position with respect to D 162
General position with respect to D|D' 165
Generalized degree formula 10 125 216
Generalized degree formula for algebraic cobordism 230
Geometric cobordism 29
Good position 162 165
Good position with respect to D 162
Good position with respect to D|D' 165
Grothendieck — Niemann — Roch theorem 6
| Grothendieck. Alexander VIII 3 93
Gysin morphism 194
Gysin morphism, functoriality 197
Gysin morphism, properties 194—197
Gysin morphism, refined 202 203
Gysin morphism, refined, functoriality 205
Higher degree formula 134 231
Hironaka, Heisuki X 119 184 233
Homotopy property as axiom 145
Homotopy property in algebraic cobordism 76 81
Iintersection homomorphism 170
Iintersection homomorphism, commutativity 182
Iintersection homomorphism, moving lemma 184
Iintersection homomorphism, refined 170
Inverse Todd class operator 97
Inverse Todd class operator, universal 99 227
l.c.i. closed admissible subcategory 142
l.c.i. morphism 141
l.c.i. morphism, pull-back for 198—200
l.c.i. scheme 143
Landweber — Novikov operations 102 130 229
Lazard ring VII 4
Lazard ring and algebraic cobordism 7 118 119
Lazard ring, grading 5
Localization property 125
Localization theorem 63
MacPherson, Robert 41
Milnor hypersurface 44
Milnor hypersurface, relation with a formal group law 44 45
Moving Lemma 190
Naive cobordism 38
Normal cone 201
Operational structure of an oriented theory 148
Oriented Borel — Moore functor 18
Oriented Borel — Moore functor and oriented cohomological functors 26
Oriented Borel — Moore functor of geometric type 26 91
Oriented Borel — Moore functor of geometric type, birational invariance 110
Oriented Borel — Moore functor of geometric type, examples 27
Oriented Borel — Moore functor with product 23
Oriented Borel — Moore functor with product, universal 24
Oriented Borel — Moore functor, detected by smooth schemes 19
Oriented Borel — Moore functor, generated by smooth schemes 19
Oriented Borel — Moore functor, quotient 25
Oriented Borel — Moore homology theory 143
Oriented Borel — Moore homology theory and oriented Borel — Moore weak homology theories 153
Oriented Borel — Moore homology theory and oriented cohomology theories 149
Oriented Borel — Moore homology theory, examples 145
Oriented Borel — Moore homology theory, operational structure 148
Oriented Borel — Moore homology theory, twisting 227—228
Oriented Borel — Moore R-functor 24
Oriented Borel — Moore weak homology theory IX 91
Oriented Borel — Moore weak homology theory, associated to an oriented Borel — Moore homology theory 153
Oriented Borel — Moore weak homology theory, associated to an oriented cohomology theory 155
Oriented Borel — Moore weak homology theory, genetically constant 123
Oriented Borel — Moore weak homology theory, twisting 99
Oriented cohomological functor 26
Oriented cohomological functor and oriented Borel — Moore functors 26
Oriented cohomological functor with product 26
Oriented cohomology theory VII 2 92
Oriented cohomology theory and oriented Borel — Moore homology theories 149
Oriented cohomology theory and oriented weak cohomology theories 152
Oriented cohomology theory, multiplicative 6
Oriented cohomology theory, ordinary 6
Oriented cohomology theory, periodic 6
Oriented weak cohomology theory IX 92
Oriented weak cohomology theory, associated to an oriented cohomology theory 152
Projective bundle X
Projective bundle formula 3
Projective bundle formula as axiom 84 85 91 144
Pseudo-divisor 160
Pseudo-divisor, defining equation 160
Pseudo-divisor, pull-back 192
Pseudo-divisor, support 160
Pull-back for pseudo-divisors 192
Pull-back, l.c.i. 198—200
Pull-back, refined 201 207
Pull-back, refined, commutativity 211
Pull-back, refined, excess intersection formula 209 211
Pull-back, refined, properties 208
Quillen's theorem VII
Quillen, Daniel VII VIII 2 14 20 83 99 102 117
Refined algebraic cobordism 160
Refined intersection 201 212
Refined pullback 201 207
Refined pullback, commutativity 211
Refined pullback, excess intersection formula 209 211
Refined pullback, properties 208
Regular embedding 141
Relative dimension 1
Resolution of singularities IX X 12 40 51 60 63 76 79 81 83 116 119—121 167 169 201 215 217 229 233—234
Rost's degree formula 134
Rost, Markus VIII 83 122 129 131
Splitting principle 85
Standard cycle 24
Strict normal crossing divisor 53
Strict normal crossing divisor, class in  218
Strict normal crossing divisor, cobordism class 53 58
Strict normal crossing divisor, cobordism class, refined 164 167
Strict normal crossing divisor, face 53
Tangent bundle of a smooth morphism 100
Tangent bundle, virtual 101 228
Todd class operator 100
Todd class operator, inverse 97
Todd class operator, inverse, universal 99
Tor-independent morphism 1
Transversality theorem 66
Transverse morphism 1
Twisting construction 99
Twisting construction, examples 101—103
Twisting construction, first form 99
Twisting construction, Grothendieck — Riemann — Roch 115
Twisting construction, Landweber — Novikov operations 102
Twisting construction, second form 101
Unoriented cobordism 13
Very good position 162 165
Very good position with respect to D 162
Very good position with respect to D|D' 165
Virtual normal bundle 100 101
Weak factorization 12 40 74 83 116 119—121 234—235
Whitney product formula 3 95
Zigzag diagram 194
Zigzag diagram, extended 203
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