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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holonomic modules, localizing class, many injective objects, cohomological descent, perverse sheaves, distinguished triangles, divisor with normal crossings, exact triples, soft sheaves, abelian category, translation functor, acyclic complex, regular singularities, ringed spaces, triangulated category, homotopic equivalence, filtered complex, derived functors, injective resolution, triangulated categories, abelian categories, continuous cohomology, zero morphism, cyclic homology, spectral sequence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bibliographic Hints, Key Lemma, Hodge A-structures, Homology of Discrete Groups, Cohomology of Infinite-Dimensional Lie Algebras, Small Dimensions New!
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holonomic modules, localizing class, many injective objects, cohomological descent, perverse sheaves, distinguished triangles, divisor with normal crossings, exact triples, soft sheaves, abelian category, translation functor, acyclic complex, regular singularities, ringed spaces, triangulated category, homotopic equivalence, filtered complex, derived functors, injective resolution, triangulated categories, abelian categories, continuous cohomology, zero morphism, cyclic homology, spectral sequence Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bibliographic Hints, Key Lemma, Hodge A-structures, Homology of Discrete Groups, Cohomology of Infinite-Dimensional Lie Algebras, Small Dimensions New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 30
books:
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- Homological Algebra (PMS-19) by Henri Cartan on page 77, and Back Matter
- Number theory, Volume 20 (Pure and Applied Mathematics) by Author Unknown in Back Matter
- Algebraic Number Theory by H. Koch in Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter
- Principles of Algebraic Geometry by Phillip Griffiths in Back Matter
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