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© 1994

Algebra V

Homological Algebra

  • A. I. Kostrikin
  • I. R. Shafarevich
  • Homological algebra is an important tool in algebraic geometry and algebraic topology

  • The book presents a modern approach to this subject taking into account applications in both these fields

Book
  • 11k Downloads

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

  • Book Title Algebra V
  • Book Subtitle Homological Algebra
  • Authors S.I. Gelfand
    Yu.I. Manin
  • Editors A.I. Kostrikin
    I.R. Shafarevich
  • Series Title Encyclopaedia of Mathematical Sciences
  • 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
  • Hardcover ISBN 978-3-540-53373-3
  • Softcover ISBN 978-3-540-65378-3
  • eBook ISBN 978-3-642-57911-0
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages V, 222
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by VINITI, Moscow, 1989 Originally published as Vol. 38 in the series: Encyclopaedia of Mathematical Sciences.
  • Topics K-Theory
    Algebraic Geometry
    Algebraic Topology
  • Buy this book on publisher's site