Homological Algebra

S.I. Gelfand, Yu.I. Manin (Autoren)

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

Buch | Hardcover

V, 222 Seiten

1994 | 1994
Springer Berlin (Verlag)
978-3-540-53373-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	29.3.1994
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Übersetzer	S.I. Gelfand, Yu.I. Manin
Zusatzinfo	V, 222 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	484 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • Algebra; Handbuch/Lehrbuch • Algebraic Geometry • algebraic topology • category theory • cohomology • D-modules • D-Moduln • gemischte Hodgestrukturen • Hodge Theory • Homological algebra • Homologische Algebra • homologischen Algebra • Homology • Kategorietherorie • mixed Hodge structures • Sheaves
ISBN-10	3-540-53373-7 / 3540533737
ISBN-13	978-3-540-53373-3 / 9783540533733
Zustand	Neuware