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Ueno K. — Algebraic Geometry. From varieties to schemes (vol. 1)
Ueno K. — Algebraic Geometry. From varieties to schemes (vol. 1)

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Название: Algebraic Geometry. From varieties to schemes (vol. 1)

Автор: Ueno K.

Аннотация:

This is the first of three volumes on algebraic geometry. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject.
The book begins with a description of the standard theory of algebraic varieties. Next, sheaves are introduced and studied, using as few prerequisites as possible, and finally, Ueno describes schemes and their properties. Further properties of schemes will be discussed in the second volume. Ueno's book is a self-contained introduction to this important circle of ideas which assumes only a knowledge of basic notions from abstract algebra (such as prime ideals).


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 154

Добавлена в каталог: 18.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$O_x$-module      77
Affine algebraic set      2
Affine algebraic variety      12 20
Affine hyper surface      13
Affine lime      13
Affine open set      72
Affine plane      13
Affine scheme      71
Affine space      2
Algebraic set      2
B&out's Theorem      38
Base change      131
Canonical projection      121
Category      101
Category theory      101
Closed immersion      96
Closed set      11
Closed subscheme      96
Commutative diagram      103
composition      101
Connected      88
Contravariant functor      104
Coordinate ring      13
Covariant functor      103
Diagonal morphism      131
Diagram      103
Direct image      79
Direct product      115
Directed set      58
Dual category      104
EQUIVALENCE      105
Etale cohomology      108
Fiber      128
Fiber product      115
Final object      112
Finite morphism      94
functor      103
Generic point      46
Geometric point      109
Geometrically integral      129
Geometrically irreducible      129
Geometrically reduced      129
Germ      60
Graded ring      86
Grothendieck topology      108
Hausdorff axiom of separation      12
Hilbert's basis theorem      3
Hilbert's Nullstellensatz      9
Homogeneous component of degree      86
Homogeneous coordinate ring      32 33
Homogeneous ideal      32 84
Homogeneous polynomial      32
Homogeneous prime spectrum      87
Homomorphism      77
Identity morphism      102
Inductive limit      58 59
Initial object      112
integral      8 89
Irreducible      12 89
Irreducible subscheme      47
Isomorphism      17 103 104
K-rational point      112
Line at infinity      35
Local intersection multiplicity      27
Local ringed space      81
localization      54
Locally Noetherian      92
Locally of finite type      94
Maximal spectrum      18
Morphism      14 101 104
Multiplicatively closed subset      54
Natural transformation      104
Nilradical      54
Noetherian      92
Object      101
Of finite type      94
Open immersion      95
Open set      11
Open subscheme      95
Order      57
Point at infinity      25 35
Prescheme      132
Presheaf      67
Prime ideal      12
Prime spectrum      43
PRODUCT      118
Projective geometry      35
Projective line      25 30
Projective plane      30
Projective scheme      88
Projective set      32
Projective space      25 30
Projective transformation      35
Projective variety      33
Quasicompact      53
R-valued point      108
Radical      4
Reduced      89
Reduced ideal      10
Reducible      12 89
Regular function      17 22
Representable      117
Residue field      111
Restriction      75
Restriction map      57
Restriction mapping      57
Ringed space      23 81
S-valued point      108
Scheme      82 83
Sheaf      25 67-69
Sheafed space      98
Sheafification      99
Stalk      72
Structure morphism      112
Structure sheaf      71
Tensor product      78
topology      11
Underlying space      71
Universal mapping property      56
Weak Hilbert's Nullstellensatz      6
Zariski cotangent space      113
Zariski tangent space      113
Zariski topology      11
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