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| Herzog B. — Kodaira-Spencer Maps in Local Algebra |
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| Предметный указатель |
 -filtration 9
-minimal 62
-minimal, with respect to (b, d) 62
 -distinguished basis 59
Algebra generators, homogeneous 115
Artin — Rees filtration 10
Associated graded ring 2
Base change 145
Base change homomorphism 145
Basic exact sequence 42
Closure 14
Cofinite 3
Compatible filtrations 9
complete 13
Completion 13
Contained in a filtration 4
Critical 163
Definable over a subalgebra 111
Defined over a subalgebra linear map 111
Defined over a subalgebra module 111
Defining equations of the deformation space 153
Defining equations of the fibre 150
Defining exact sequence for  14
Defining exact sequence for cl(N) 14
Defining exact sequence for in(I) 9
Defining ideal 103
Defining submodule 111
Deformation x
Deformation, embedded germ 145
Deformation, germ ix
Deformation, space, defining equations 153
Deformations, embedded of first order 157
Deformations, functor of embedded 157
Degree 1
Degreewise lexicographic order 148
Derivations 103
Direct image filtration 7 9
Distinguished basis 59
Embedded deformation functor 157
Embedded deformation germ 145
Embedded deformations 157
Embedded first order deformations 157
Embedded Kodaira — Spencer map 106
Embedding of a permissible graded homomorphism 106
Exact sequence associated with a family 33
Exact sequence, basic 42
Exact sequence, defining for  14
Exact sequence, defining for cl(N) 14
Exact sequence, defining for in(I) 9
Exponential Hilbert series 133
F-distinguished basis 59
Family associated exact sequence 33
Family generating a filtration 7
Family of structure constants 118
Filtered module 8
Filtered module homomorphism 8
Filtered ring 2
Filtration 2 8
Filtration, contained in another one 4
Filtration, direct image of 7 9
Filtration, generated by a family 7
Filtration, ideal-adic 3 10
Filtration, induced on a factor ring 7
Filtration, induced on a subring 6
Filtration, inverse image of 6 9
Filtration, minimal 62
Filtration, q-adic 4
Filtration, quasi-homogeneous 4
Filtration, weight 4
Finite Hilbert function 76
Flatifying, filtration 91
Flatifying, prefiltration 91
Formal degree 163
Generating a filtration 7
Graded module 1
Graded module, homomorphism 2
Graded module, with finite Hilbert function 76
Graded ring 1
Graded ring, homomorphism 2
Graduationally flat x
Hausdorff 3
Hilbert scheme 143
Hilbert series exponential 133
Hilbert series of a filtered ring 76
Hilbert series of a graded module 76
Hilbert series of a homomorphism 77
| Hilbert — Samuel series of a filtered ring 77
Hilbert — Samuel series of a graded module 76
Hilbert — Samuel series of a homomorphism 77
Homogeneous 1
Homogeneous, algebra generators 115
Homogeneous, syzygy 31
Homomorphism of embedded deformation germs 145
Homomorphism of filtered modules 8
Homomorphism of filtered rings 3
Homomorphism of the associated graded rings 3
I-adic filtration 3 10
Ideal 9
Ideal-adic filtration of a module 10
Ideal-adic filtration of a ring 3
Image filtration 6 9
Inclusion of filtrations 4
Induced 6 7
Induced filtration on a factor ring 7
Induced filtration on a subring 6
Initial element 9
Initial form 9 148
Intersection of filtrations 4
Inverse image 9
Irrelevant entry 163
Irrelevant ideal 1
Kodaira — Spencer map 108
Kodaira — Spencer map, embedded 106
Krull dimension 77
Lech's problem 78
Liftable to a syzygy 31
Local singularity x
Minimal 115 116
Minimal, flatifying prefiltration 93
Minimal, over a filtration 62
Minimal, w.r.t. a distinguished basis 62
Module filtration 8
Monomial lift 118
Monomial module generators 116
Multiplicity 77
Natural filtration 3
Natural topology 3
Nice distinguished basis 117
Non-standard degree 151
Normal module 103
Normally flat 101
Order degreewise lexicographic 148
Order in a filtered module 9
Order in a filtered ring 2
Order total 76
Permissible graded algebra 101
Permissible graded homomorphism 101
Permissible graded homomorphism, embedding of 106
Point functor 143
Prefiltration 39
q-adic filtration 4
Quasi-homogeneous filtration 4
refinement 14 21
Residually rational xvi
Residually separable xvi
Ring filtration 2
Russian conjecture 141
Schlessinger's  103
Separated 3
Shifting degrees 2
Special fibre x 7
Standard basis 30
Standart monomial 148
Strict homomorphism 32
Strict system of generators 30
Stronger 21
Structure constants 66 117 150
Sum of filtrations 5
Sum transform 76 77
Syzygy 31
Tangent space 157 158
Tangentially flat x 3
Total order 76
Underlying lifts 117
Underlying system of algebra generators 117
Underlying system of module generators 117
Underlying vector space basis 117
Universal germ 147
Weaker 21
Weakly graded 102
Weight filtration 4
Zariski tangent space 157 158
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