Algebra V : homological algebra

Contributor(s): Edited by A. I. Kostrikin | I. R. ShafarevichMaterial type: TextTextSeries: Encyclopaedia of Mathematical Sciences ; Volume 38Publication details: Heidelberg: Springer-Verlag, [c1994]Description: 222 pISBN: 9783540653783LOC classification: QA169Online resources: Click here to access online
Contents:
Introduction 1. Complexes and Cohomology 2. The Language of Categories 3. Homology Groups in Algebra and in Geometry 4. Derived Categories and Derived Functors 5. Triangulated Categories 6. Mixed Hodge Structures 7. Perverse Sheaves 8. D-Modules
Summary: This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology. --- summary provided by publisher
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 4 QA169 (Browse shelf (Opens below)) Available Billno: 42976 ; Billdate: 29.03.2019 01940
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Introduction
1. Complexes and Cohomology
2. The Language of Categories
3. Homology Groups in Algebra and in Geometry
4. Derived Categories and Derived Functors
5. Triangulated Categories
6. Mixed Hodge Structures
7. Perverse Sheaves
8. D-Modules

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology. --- summary provided by publisher

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