書誌事項

Homological algebra

A.I. Kostrikin, I.R. Shafarevich (eds.)

(Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 38 . Algebra ; 5)

Springer-Verlag, c1994

  • : gw
  • : us

タイトル別名

Algebra

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注記

"Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamental'nye napravleniya, vol. 38, Algebra 5"--T.p. verso

Includes bibliographical references and indexes

内容説明・目次

内容説明

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.

目次

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.- References.- Author Index.

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詳細情報

  • NII書誌ID(NCID)
    BA22329852
  • ISBN
    • 3540533737
    • 0387533737
  • LCCN
    93033442
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    rus
  • 出版地
    Berlin ; New York
  • ページ数/冊数
    222 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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