This volume of the Encyclopaedia presents a modern approach to homological algebra, which is 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 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 famousfor his work in algebraic geometry and mathematical physics. The book isan excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geomtry and algebraictopology.
Introduction.- Complexes and Cohomology.- The Language of Categories.- Homology Groups in Algebra and in Geometry.- Derived Categories and Derived Functors.- Triangulated Categories.- Mixed Hodge Structures.- Perverse Sheaves.- D-Modules.- References.- Indices.
Series: Encyclopaedia of Mathematical Sciences
Number Of Pages: 222
Published: September 2009
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5
Weight (kg): 0.51