《代數幾何II：代數簇的上同調，代數曲面》是2007年1月1日科學出版社出版的圖書，作者是I.R.Shafarevich。
基本介紹
內容簡介,目錄,
內容簡介
《國外數學名著系列（影印版）34：代數幾何2 代數簇的上同調，代數曲面》由兩部分構成，前半部分著重介紹代數簇的上同調，後半部分討論代數曲面。《國外數學名著系列（影印版）34：代數幾何2 代數簇的上同調，代數曲面》還包含涉及不同主題的大量例子和見解。作者均為該領域的著名專家，他們盡其所能地嚴謹而系統地闡述了這些論題。
《國外數學名著系列（影印版）34：代數幾何2 代數簇的上同調，代數曲面》對研究代數幾何及算術代數的數學家和研究生都將大有裨益。
目錄
Introduction
Chapter1．Homological Machinery
1．Origins of Homological Concepts
1．1 the Idea of Homology
1．2 Homology of Triangulated Spaces
1．3 Singular Homology
1．4 Cohomology
1．5 Sheaves
1．6 Cohomology of Shaves
1．7 Cohomology of Coherent Sheaves
1．8 Cohomology of Etale Sheaves
2 Complexes
2．1 Exact Sequences
2．2 Complexes
2．3 A Long Exact Sequence
2．4 Filtred Complexes
2．5 Spectral Sequences
2．6 Bicomplexes
2．7 Mapping Cone
2．8 Products
3．Sheaves
3．1 Presheaves
3．2 Sheaves
3．3 Direct and Inverse Images of Sheaves
3．4 Abelian Sheaves
3．5 Flabby Sheaves
4．Cohomology of Sheaves
4．1 Construction of Cohomology
4．2 Hypercohomology
4．3 Higher Direct Images
4．4 Cohomology of a Covering
4．5 The Acyclicity Criterion for Coverings
Chapter2．Cohomology of Coherent Sheaves
1．Cohomology of Quasi-Coherint Sheaves
2．Cohomology of Projective Space
3．Cohomology of Proper Morphisms
4．The Riemann-Roch Theorem
5．Duality
6．The de Rham Cohology
Chapter3．Cohomology of Complex Varieties
1．Complex Varieties as Topological Spaces
2．Cohomology of Coherent Sheaves
3．Weights in Cohomology
4．Algebraic Approach to Classical Topolpgy
Chapter4．Etale Cohomology
1．The Weil Conjectures
2．Algebraic Fundamental Group
3．Etale Topology
4．Cohomology of Etale Sheaves
5．Cohomology of Algebraic Curves
6．Fundamental Theorems
7．l-Adic Cohomology
8．Deligne's Theorem
Bibliography
References
