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Knutson D. — Algebraic spaces
Knutson D. — Algebraic spaces

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Название: Algebraic spaces

Автор: Knutson D.

Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 261

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"Open subspace where a scheme"      133
Affine etale covering      103
Affine formal scheme      211
Affine image of a map      124
Algebraic space      92
Algebraic space is a scheme      104
Algebraic space, affine      104
Algebraic space, formal      215
Algebraic space, integral      144
Algebraic space, irreducible      127
Algebraic space, locally noetherian      105
Algebraic space, locally separated      97
Algebraic space, n-dimensional      97
Algebraic space, noetherian      105
Algebraic space, nonsingular      106
Algebraic space, normal      106
Algebraic space, quasicompact      105
Algebraic space, reduced      106
Algebraic space, separated      97
Algebrizable$_X$-module      247
Ample invertible sheaf      142
atom      133
Axiom $A_0$      30
Axioms $S_1,S_2,S_3(a),S_3(b)$      36
Blowing up      19
Chevalley's Theorem      169
Chow's Lemma      190
Closed subcategory      32
Closure, geometric      124
Closure, scheme-theoretic      48
Coherent sheaf      41
Cohomology of sheaves (quasicoherent)      117
Completeness Lemma      155
Completion of a ring along an ideal      210
Completion of an algebraic space along a closed subspace      216
Components of a space      145
Connectedness Theorem      233
Covering map      30
Covering, affine etale      103
Covering, representable etale      92
Curve      236
Decomposition into components      145
Dense, geometrically      124
Dense, topologically      125
Descent theory for modules      54
Descent theory for modules over adic rings      207
Descent, effective      32
Devissage      173
Diagonal component      6 80
Dimension, codimension of a point      236
Divisor, Cartier      149
Divisor, Weil      240
Eequivalence relation, "finitely presented"      83
Eequivalence relation, categorical      72
Eequivalence relation, effective      72
Eequivalence relation, induced      72
Eequivalence relation, on algebraic spaces      113
Eequivalence relation, quotient of      72
Effective descent      32 34
Etale covering,representable      92
Etale topology, affine formal schemes      211
Etale topology, algebraic spaces      102
Etale topology, schemes      59
Extension Lemma      157
Fiber of a quasicoherent sheaf at a point      148
Filtration, I-good      220
Finiteness theorem      203
Flat topology, affine schemes      58
Flat topology, schemes      58
Formal algebraic space      215
Formal algebraic space, general definitions      215
Formal algebraic space, ideal of definition      217
Formal scheme as formal algebraic space      216
Formal scheme, affine      211
Function field      148
Function field sheaf      148
Generic point      144
Generic rank of a coherent sheaf      150
Geometric closure      124
Geometrically dense      124
Gluing data      5
Graded R-module      219
Graded ring      218
Grothendieck Existence Theorem      247
Grothendieck topology      29
Group actions on an algebraic space      177
Group actions on an algebraic space, fixed point locus      186
Group actions on an algebraic space, free action      178
Group actions on an algebraic space, geometric quotient of      178
Hilbert basis theorem      108
Hilbert scheme      2
Holomorphic Functions Theorem      227
Immersion, closed      42
Immersion, open      42
Inductive property of algebraic spaces      128
Invertible sheaf      42
Jacobian condition      59
Local construction      33
Local construction, effective      33
Local on the domain      32 33
Local ringed space      39
Locally separated      97
Map = morphism, map of adic rings      205
Map = morphism, map of adic rings, adic      205
Map = morphism, map of adic rings, faithfully flat      207
Map = morphism, map of adic rings, flat      207
Map = morphism, map of adic rings, formal etale covering      208
Map = morphism, map of adic rings, formally etale      208
Map = morphism, map of adic rings, of finite type      207
Map of affine formal schemes      211
Map of affine formal schemes, closed imbedding      211
Map of affine formal schemes, imbedding      211
Map of affine formal schemes, open imbedding      211
Map of algebraic spaces      92
Map of algebraic spaces of finite presentation      107
Map of algebraic spaces of finite type      107
Map of algebraic spaces, affine      108
Map of algebraic spaces, birational      144
Map of algebraic spaces, closed      133
Map of algebraic spaces, closed immersion      108
Map of algebraic spaces, covering map      101
Map of algebraic spaces, etale      101
Map of algebraic spaces, etale surjective      101
Map of algebraic spaces, faithfully flat      107
Map of algebraic spaces, finite      139
Map of algebraic spaces, flat      107
Map of algebraic spaces, immersion      108
Map of algebraic spaces, locally of finite presentation      107
Map of algebraic spaces, locally of finite type      107
Map of algebraic spaces, locally quasifinite      107
Map of algebraic spaces, locally separates      109
Map of algebraic spaces, projective      141
Map of algebraic spaces, quasiaffine      108
Map of algebraic spaces, quasicompact      105
Map of algebraic spaces, quasifinite      107
Map of algebraic spaces, quasiprojective      141
Map of algebraic spaces, quasiseparated      109
Map of algebraic spaces, reduced closed immersion      109
Map of algebraic spaces, section of      110
Map of algebraic spaces, separated      109
Map of algebraic spaces, Stein      123
Map of algebraic spaces, surjective      107
Map of algebraic spaces, universally closed      133
Map of algebraic spaces, universally open      107
Map of algebraic spaces,open immersion      108
Map of formal algebraic spaces, general definitions      215 216
Map of formal algebraic spaces, proper      218
Map of local ringed spaces      39
Map of rings, faithfully flat      53
Map of rings, flat      53
Map of schemes      40
Map of schemes of finite presentation      56
Map of schemes of finite type      56
Map of schemes, affine      47
Map of schemes, bijective      43
Map of schemes, closed      43
Map of schemes, etale      59
Map of schemes, faithfully flat (fflat)      50
Map of schemes, finite      50
Map of schemes, flat      56
Map of schemes, formally etale      61
Map of schemes, injective      43
Map of schemes, locally of finite      43
Map of schemes, locally of finite presentation      46
Map of schemes, open      43
Map of schemes, quasicompact      45
Map of schemes, quasifinite      47 56
Map of schemes, quasiseparated      46
Map of schemes, radiciel      43
Map of schemes, separated      44
Map of schemes, surjective      44
Map of schemes, union of Zariski, open sets      44
Map of schemes, universally bijective      43
Map of schemes, universally closed      43
Map of schemes, universally injective      43
Map of schemes, universally open      43
Map of schemes, unramified      61
Map of schemes, Z-open      44
Modification      14
Module over radic ring, complete Hom set      200
Module over radic ring, complete tensor product      200
Module over radic ring, continuous      209
Moisezon Space      23
Nittag — Leffler condition      221
Noetherian Induction      128
Picard group      150
POINTS      129
Points, equivalence of      129
Points, generic      144
Points, geometric      129
Points, residue field at      126
Points, schemelike      131
Presheaf      30
Prime spectrum      38
Projective n-space over an algebraic space      141
Quasicoherent sheaf      42
Quasicoherent sheaf, in the etale topology      67
Quasicompact (scheme)      41
Rank of a locally free sheaf      42
Rank, generic, of a coherent sheaf      150
Representable etale covering      92
Ring, adic      204
Ring, associated graded      219
Ring, discrete adic      205
Ring, graded      218
Scheme      41
Scheme, affine      40
Scheme, locally noetherian      49
Scheme, Noetherian      45
Scheme, nonsingular      45
Scheme, of dimension n over a ground field      45
Scheme, reduced      45
Scheme, separated      44
Section of a map      110
Serre Criterion      163
Serre Criterion, Weak      161
Serre Finiteness Theorem      142
Sheaf Criterion for Isomorphism      121
Sheaf on an algebraic space, coherent      113
Sheaf on an algebraic space, continuity      212
Sheaf on an algebraic space, locally free of rank r      113
Sheaf on an algebraic space, map of      113
Sheaf on an algebraic space, quasicoherent      113
Sheaf on an algebraic space, structure      213
Sheaf, abelian      30
Sheaf, coherent      41
Sheaf, global, on the category of affine formal schemes      212
Sheaf, Hom and Ext      241
Sheaf, invertible      42
Sheaf, quasicoherent      42
Sheaf, structure      104
Sheaf, torsion      151
Sheaf, torsion-free      151
Space, local ringed      39
Spec R      38
Spectrum      38
Sseparated algebraic space      97
Stable (class of maps)      32
Stable, (class of objects)      31
Stable, (property of maps)      34
Stable, (property of objects)      34
Stalk      148
Stalk, geometric      147
Stein factorization of a map      124 Also see p. 233
Strict initial object      35
Strict projective system      221
Subcategory, closed      32
Subscheme      41
Subscheme, closed      40
Subscheme, open      40
Subspace of an algebraic space      109
Subspace, closed      109
Subspace, open      109
Support of a sheaf on a scheme      52
Support of a sheaf on an algebraic space      127
surface      236
Symmetric powers of projective spaces      188
Symmetric powers, effective      73
Symmetric powers, equivalence relation      73
Symmetric powers, quotient      73
Topologically dense      125
topology      29
Topology associated to a closed subcategory      35
Topology, affine formal schemes      211
Topology, algebraic spaces      102
Topology, etale, local vs. global      102
Topology, flat (schemes)      55
Topology, fppf (schemes)      59
Topology, schemes      63
Topology, Zariski, on an algebraic space      132
Topology, Zariski, on schemes      44
Truncation, of a formal algebraic space      217
Truncation, of adic ring      205
Universal effectively epimorphic family (UEEF)      34
Variety      235
Variety, dimension of      236
Variety, prevariety      235
Zariski topology on an algebraic space      132
Zariski topology on schemes      44
Zariski's Nain Theorem      235
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