Homological Algebra

by Igor R. Shafarevich

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.

227 pages, Hardcover

First published June 22, 1999

About the author

Igor Rostislavovich Shafarevich is a Russian mathematician who has contributed to algebraic number theory and algebraic geometry. He has written books and articles that criticize socialism and was an important dissident during the Soviet regime.