代數(shù)幾何II

內(nèi)容概要

本書由兩部分構(gòu)成，前半部分著重介紹代數(shù)簇的上同調(diào)，后半部分討論代數(shù)曲面。本書還包含涉及不同主題的大量例子和見解。作者均為該領(lǐng)域的著名專家，他們盡其所能地嚴(yán)謹(jǐn)而系統(tǒng)地闡述了這些論題。    本書對(duì)研究代數(shù)幾何及算術(shù)代數(shù)的數(shù)學(xué)家和研究生都將大有裨益。

書籍目錄

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

圖書封面

圖書標(biāo)簽Tags

無

評(píng)論、評(píng)分、閱讀與下載

---

    代數(shù)幾何II PDF格式下載

---