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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