Tennison B.R., Hitchin N.J. (Ed) — Sheaf Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Tennison B.R., Hitchin N.J. (Ed) — Sheaf Theory

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Название: Sheaf Theory

Авторы: Tennison B.R., Hitchin N.J. (Ed)

Аннотация:

Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based on a lecture course for graduate pure mathematicians which builds up enough of the foundations of sheaf theory to give a broad definition of manifold, covering as special cases the algebraic geometer's schemes as well as the topological, differentiable and analytic kinds, and to define sheaf cohomology for application to such objects. Exercises are provided at the end of each chapter and at various places in the text. Hints and solutions to some of them are given at the end of the book.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2007

Количество страниц: 171

Добавлена в каталог: 25.04.2008

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Предметный указатель

      2 25
$C^n(\mathcal{U}, F)$       140
, , $C^{\omega}$       2
$C_1(\mathcal{U}, F)$       153
      119 141
$E\pi E$       25 74
      144
,       63
      8 34
      65 152
      31
      56
$Hom_{\phi}(-, -)$       56
      130
      132
$H^n(\mathcal{U}, -)$       141
      138
      131
$H^n_{\Phi}(X, -)$       140
      68
      35
      87
      34
      22 34
      3 9 14 18
      3 13 17
      123
$R^n\Phi_*$       133
$R^{\dot}F$       125
      82
      84
      54 109 110
      8
$T^{\dot}$ , a      124
$U_{\sigma}$ , ( $s_{\sigma}$ )      140
$Z^1(\mathcal{U}, -)$       150
$\bot$       vii 48
$\gamma$       18 34
$\Gamma(U, E)$       18 27 28 36
$\Gamma(U, f)$       36
$\Gamma_{\phi}$       140
$\hat{H}^n(X, -)$       142
$\hat{s}$       21
$\hat{\otimes}$       108
$\leq$       3 32 40 143
$\lim$       5
$\mapsto$ , $\cong$       vii
$\mathbb{N}$ , $\mathbb{Z}$ , $\mathbb{Q}$ , $\mathbb{R}$ , $\mathbb{C}$       vii
$\mathcal{K}^q(F)$       147 153
$\mathcal{O}$       29 74 84
$\mathcal{O}$ -Mod      96
$\mathcal{O}^*$       150
$\mathcal{O}_X(n)$       107 110
$\mathcal{U}^{op}$       37 69 71
$\oplus$       47 97
$\otimes$       98
$\partial$       124 126
$\partial$ -functor      124 129 132 143 147 152
$\phi^*$       57 69
$\phi_*$       53 69
$\Phi_*$ , $\Phi^*$       101
$\pi$       25 48 74
$\rho^U_V$       1
$\rho_{\alpha\beta}$       3
$\tilde{M}$       96
$\underline{End}$       114
$\underline{Hom}(-, -)$       70 100 105
A      85 111 112
Abelian category      35 49
Abelian sheal      15
Acyclic      119 129 153
Additive category      37 49
Additive functor      71
Adjoint functors      37 60 61 94 101 114 117
Affine morphism      112
Affine scheme      84 87 89 104 109 112
Affine space      85 111 112
Algebra      73 111
Algebraic curve      106 111
Algebraic functions      29 85
Analytic functions      2 27 30 44 52 76 88 89 93
Associated sheaf      22 134
Associativity      32
Automorphisms      103 124
Bilin(-, -, -)      99
Bilinear map      99
Biproduct      47
Category      31 37 49
Cech      141 142
Classifying map      71
Coboundary      151
Cochain      153
Cocycle      150
Coequaliser      69
Cohomology      119 129 130 132 139 140 141 142 147
Cokernel      41 42
Colimit      69 98
COMPLEX      119
composition      10 31 76
Constant functor      35
Constant presheaf      2 9 24 36
Constant sheaf      24—25 28
Continuous functions      2 17 18 25 27 58 75
Contravariant functor      33
Conventions      vii 27 33 36 73
Coproduct      48 97
Covariant functor      33
CURVES      111
Derived functor      123 144 152
Differentiable functions      2 27 75 87 88
Dihomomorphism      95
Direct image      53 54 60—61 68 69 75 80 101 133 137
Direct limit      4—8 98
Direct product      48 97
Direct sum      8 47 97—98
Direct system      3 7 33 35
Directed set      3 35
Disjoint union      vii 6
Dual category      37 69 71
Dual sheaf      105
Effaceable      128 145 152
End, Aut      103
Endomorphisms      103 114 131 136
Epimorphism      10 43 46 69 78
Equaliser      15 69
Equivalence relation      69
Evaluation map      70 105
Exact $\partial$ -functor      124 128 143 146 147 152 158
Exact complex      119
Exact functor      51 61 62 65 116 129—130 143
Exact sequence      12 16 50 53
Extension by zero      62—63 68 135 152
Fibre      17 19
Finite presentation      114
Finite type      113
Flasque      137
Flat      137

Forgetful functor      33
functor      33
Functoriality      11 20 21 54
F|U      28 62 99
Geometric space      87
Germ      9 27 100
Glueing condition      14
GSP      93
H(g), g*      120
Half exact functor      71
Hom(-, -)      31 36
Hom-sheaf      70 100 105 114
Homogeneous coordinates      110
Homotopic      119
Homotopy equivalent      122
Identity      32 35
Image      49 79
Injective object      116 118 119 123 132 135 138 144 145
Inverse image      57 60—61 68 69 75 80 101
Inverse limit      12
Invertible      105 149
Isomorphism      10 44 76
K-Presh      34 72
Ker(f)      38
Kernel      38 40
L      21 34
L, ,       119
Left exact      35 51 55 62 122 125
LIMIT      12 69
Local homeomorphism      18
Local morphism      86
Local ring      29 84
Localisation      84
Locally closed      63
Locally connected      28
Locally free      72 102 104 112
Locally isomorphic      89
Manifold      90—91 151
Module      94 95
Monomorphism      10 38—39 69 78
Monopresheaf      14 72 144
Mor      32
Morphism      31
Morphism of $\partial$ -functors      124 143
Morphism of complexes      119
Morphism of geometric spaces      87
Morphism of manifolds      90
Morphism of modules      94 95
Morphism of presheaves      9 33
Morphism of R-algebras      73
Morphism of ringed spaces      76
Morphism of sheaf spaces      18 26 33
Morphism of sheaves      17 33
Morphism over a continuous map      55
Morphism over a ring morphism      95
Natural      23 34
Natural equivalence      35
Natural isomorphism      5 23 35 100
Natural transformation      34 57
OB      31
Objects      31
P      107 109—110
PCok(f)      41
PIC      105
Picard group      105 107 149—151
PIm(f)      49
Preadditive category      37
Preordered set      3 32
Presh, Shv, Shfsp      33 37
Presheaf      1 34 69 71 72
Presheaf cokernel      41
Presheaf image      49
Presheaf morphism      9
Prime ideal      81
Prime spectrum      81
PRODUCT      48 97—98
Projective      104
Projective space      106 109—110
Quasi-coherent      96 111 147
Quotient      46 69
R-alg      74
R-Mod      94
Rational functions      29
refinement      141
Representable functor      68
Resolution      119 138
Restriction      28 62 99 102
Restriction map      1 95
Riemann surface      90 106
Right exact      51 62 116
Ring      73
Ringed space      74
S/X, P/X      69 70
Scheme      90 147
SCok(f)      42
Sections      1 27 28 52
Separated presheaf      14
Separated scheme      91
Sets, Abgp, Top      32
Sheaf      15 69 72 74
Sheaf cokernel      42
Sheaf image      49
Sheaf of ideals      78 80
Sheaf of sections      17 18
Sheaf space      18 26 74
Sheafification      22 34 35 52 61 144
Sheaves of functions      2 9 14 17 27 29 75 76 85 87
SIm(f)      49
simplex      140
Singular cohomology      147
Spec      112
SpecR, V(a), D(f)      81
Spectral sequence      139 147 152
Sphere      54 109 110
Split      116 125 157
Stalk      8 10 19 21 23 40 45 58 80
Structure map      18 73
Structure sheaf      74
Subobject      40
Subobject classifier      70
Subpresheaf      39
Subsheaf      39
SUM      8 36 47 97—98
Supports      139 147
TARGET      4 7 35
Tensor product      98—99 105 108
Topos      71
Torsion      12
Total tensor product      108
V      112
Variety      90
Vector bundle      96 104 112
Zariski topology      82
Zero morphism      36
Zero sheaf      36
ZG, kG,       130
[0,n], , $\partial_m$       140

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