- 代数几何(第2卷)(英文版)
- - 作者：(美)大卫·曼福德//(日)小田忠雄|责编:董心意//陈亮
  - 出版社：世图出版公司
  - ISBN：9787523230107
  - 出版日期：2026/01/01
  - 页数：504
- 售价：35.2

内容大纲
全书共9章，系统介绍代数几何相关知识。首先定义了概型和层，涵盖Spec（R）、概型的积、拟凝聚层等内容，并给出层论附录与习题。接着探索概型世界，阐述经典簇作为概型的性质、闭子概型等。对ProjR进行初等全局研究，涉及可逆层、爆破等。之后探讨基域和基环，分析伽罗瓦理论与概型等。还区分了奇异与非奇异情况，介绍正则性、卡勒微分等。讲解群概型及其应用，以及凝聚层的上同调，包含基本Cech上同调、上同调计算方法等。最后给出上同调应用及两个深入结果，如黎曼－罗赫定理、森重文的有理曲线存在定理等，书末附有参考文献和索引，便于读者深入学习。
作者介绍
目录
Preface
1  Schemes and sheaves: definitions
  1.1  Spec(R)
  1.2  M
  1.3  Schemes
  1.4  Products
  1.5  Quasi-coherent sheaves
  1.6  The functor of points
  1.7  Relativization
  1.8  Defining schemes as functors
  Appendix: Theory of sheaves
  Exercises
2  Exploring the world of schemes
  2.1  Classical varieties as schemes
  2.2  The properties: reduced, irreducible and finite type
  2.3  Closed subschemes and primary decompositions
  2.4  Separated schemes
  2.5  Proj R
  2.6  Proper morphisms
  Exercises
3  Elementary global study of Proj R
  3.1  Invertible sheaves and twists
  3.2  The functor of Proj R
  3.3  Blowups
  3.4  Quasi-coherent sheaves on Proj R
  3.5  Ample invertible sheaves
  3.6  Invertible sheaves via cocycles, divisors, line bundles
  Exercises
4  Ground fields and base rings
  4.1  Kronecker's big picture
  4.2  Galois theory and schemes
  4.3  The Frobenius morphism
  4.4  Flatness and specialization
  4.5  Dimension of fibres of a morphism
  4.6  Hensel's lemma
  Exercises
5  Singular vs. non-singular
  5.1  Regularity
  5.2  Kahler differential
  5.3  Smooth morphisms
  5.4  Criteria for smoothness
  5.5  Normality
  5.6  Zariski's Main Theorem
  5.7  Multiplicities following Well
  Exercises
6  Group schemes and applications
  6.1  Group schemes
  6.2  Lang's theorems over finite fields
  Exercises
7  The cohomology of coherent sheaves

  7.1  Basic Cech cohomology
  7.2  The case of schemes: Serre's theorem
  7.3  Higher direct images and Leray's spectral sequence
  7.4  Computing cohomology (1): Push f" into a huge acyclic sheaf
  7.5  Computing cohomology (2): Directly via the Cech complex .
  7.6  Computing cohomology (3): Generate Jr by "known" sheaves
  7.7  Computing cohomology (4): Push 5r into a coherent acyclic sheaf
  7.8  Serre's criterion for ampleness
  7.9  Functorial properties of ampleness
  7.10  The Euler characteristic
  7.11  Intersection numbers
  7.12  The criterion of Nakai-Moishezon
  7.13  Seshadri constants
  Exercises
8  Applications of cohomology
  8.1  The Riemann-Roch theorem
  Appendix: Residues of differentials on curves
  8.2  Comparison of algebraic with analytic cohomology
  8.3  de Rham cohomology
  8.4  Characteristic p phenomena
  8.5  Deformation theory
  Exercises
9  Two deeper results
  9.1  Mori's existence theorem of rational curves .
  9.2  Belyi's three-point theorem
References
Index

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目