Algebraic geometry /
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ISBN:9787302140801
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简介
In spirit, this book is closer to Elements de Geometrie Algebrique (EGA) than the existing textbooks on algebraic geometry. It prvides an introduction to schemes, formal schemesc coherent sheaves, and their cohomologies. The prerequisites for reading this book is the knowledge of commutative algebra up to the level of Ateyah-Macdonald's book. The material on algebraic geometry covered in this book provides adequate preparation for reading more advanced books such as Seminaire de Geometrie Algebrique (SGA). ...
目录
1 schemes and coherent sheaves 1.
1.1 presheaves and sheaves 1
1.2 schemes and morphisms 17
1.3 properties of schemes and morphisms 28
1.4 coherent sheaves 58
1.5 formal completions of schemes and sheaves 92
2 cohomology 118
2.1 derived functors 118
2.2 spectral sequences 152
2.3 ?ech cohomology 172
2.4 cohomology of affine and projective schemes 184
2.5 cohomological study of proper morphisms 199
2.6 local freeness of higher direct images 214
2.7 grothendieck's existence theorem 231
bibliography 257
index 258...
1.1 presheaves and sheaves 1
1.2 schemes and morphisms 17
1.3 properties of schemes and morphisms 28
1.4 coherent sheaves 58
1.5 formal completions of schemes and sheaves 92
2 cohomology 118
2.1 derived functors 118
2.2 spectral sequences 152
2.3 ?ech cohomology 172
2.4 cohomology of affine and projective schemes 184
2.5 cohomological study of proper morphisms 199
2.6 local freeness of higher direct images 214
2.7 grothendieck's existence theorem 231
bibliography 257
index 258...
Algebraic geometry /
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