Algebra V

Homological Algebra

  • A. I. Kostrikin
  • I. R. Shafarevich

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 38)

Table of contents

  1. Front Matter
    Pages i-3
  2. A. I. Kostrikin, I. R. Shafarevich
    Pages 4-7
  3. A. I. Kostrikin, I. R. Shafarevich
    Pages 8-21
  4. A. I. Kostrikin, I. R. Shafarevich
    Pages 22-52
  5. A. I. Kostrikin, I. R. Shafarevich
    Pages 52-86
  6. A. I. Kostrikin, I. R. Shafarevich
    Pages 86-120
  7. A. I. Kostrikin, I. R. Shafarevich
    Pages 121-139
  8. A. I. Kostrikin, I. R. Shafarevich
    Pages 140-163
  9. A. I. Kostrikin, I. R. Shafarevich
    Pages 163-173
  10. A. I. Kostrikin, I. R. Shafarevich
    Pages 173-210
  11. Back Matter
    Pages 211-224

About this book

Introduction

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.

Keywords

D-modules Homological algebra Kategorietherorie category theory d-Moduln gemischte Hodgestrukturen homologischen Algebra mixed Hodge structures algebra algebraic geometry algebraic topology cohomology Hodge theory homological algebra homology sheaves

Editors and affiliations

  • A. I. Kostrikin
    • 1
  • I. R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-57911-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-65378-3
  • Online ISBN 978-3-642-57911-0
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site