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  • Book
  • © 1994

Homological Algebra

Editors:

  1. A. I. Kostrikin

    1. Steklov Mathematical Institute, Moscow, Russia

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    You can also search for this editor in PubMed   Google Scholar

  2. I. R. Shafarevich

    1. Steklov Mathematical Institute, Moscow, Russia

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    You can also search for this editor in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-3
    PDF

  2. Introduction

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 4-7

  3. Complexes and Cohomology

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 8-21

  4. The Language of Categories

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 22-52

  5. Homology Groups in Algebra and in Geometry

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 52-86

  6. Derived Categories and Derived Functors

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 86-120

  7. Triangulated Categories

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 121-139

  8. Mixed Hodge Structures

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 140-163

  9. Perverse Sheaves

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 163-173

  10. D-Modules

    • A. I. Kostrikin, I. R. Shafarevich
    Pages 173-210

  11. Back Matter

    Pages 211-224
    PDF
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About this book

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.
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Keywords

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Editors and Affiliations

  • Steklov Mathematical Institute, Moscow, Russia

    A. I. Kostrikin, I. R. Shafarevich

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Bibliographic Information

  • Book Title: Homological Algebra

  • Editors: A. I. Kostrikin, I. R. Shafarevich

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-642-57911-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Hardcover ISBN: 978-3-540-53373-3Published: 29 March 1994

  • Softcover ISBN: 978-3-540-65378-3Published: 20 May 1999

  • eBook ISBN: 978-3-642-57911-0Published: 01 December 2013

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: V, 222

  • 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

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Access via your institution

Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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