代数几何II
2007-1
科学
沙法列维奇
262
无
本书由两部分构成，前半部分着重介绍代数簇的上同调，后半部分讨论代数曲面。本书还包含涉及不同主题的大量例子和见解。作者均为该领域的著名专家，他们尽其所能地严谨而系统地阐述了这些论题。 本书对研究代数几何及算术代数的数学家和研究生都将大有裨益。
IntroductionChapter1.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 The Acyclicity Criterion for CoveringsChapter2.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 TopolpgyChapter4.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 TheoremBibliographyReferences
无
代数几何II是科学出版社出版的国外数学名著系列中的一部,这个系列是由国内著名数学家和中国科学院院士组成的编委会精心筛选的,都是高水平的数学精品.印刷纸张装帧都是上乘.
代数几何全面权威的参考书,不用多说了吧