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Gelfand; Yuri I. Methods of Homological Algebra.
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Gelfand ; Yuri I. Publisher: Springer Verlag , This specific ISBN edition is currently not available. View all copies of this ISBN edition:.
Synopsis About this title Provides the modern approach to homological algebra, based on the systematic use of language and ideas of derived categories and derived functors. Language Notes : Text: English translation Original Language: Russian Review : From the reviews of the second edition: "This is the revised edition of a modern approach to homological algebra by two leading writers in the field.
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Other Popular Editions of the Same Title. Search for all books with this author and title. Customers who bought this item also bought. Stock Image. Gelfand; Y. I am wondering which parts of homological algebra are mainly used in algebraic geometry; I actually know something about homological algebra and I would appreciate it if somebody could point out the methods used in algebraic geometry, and the role which they play in the development of the theory.
Methods of Homological Algebra
I am particularly interested in derived categories and the derived category approach to derived functors in contrast to the classical definition ; apparently these concepts were somehow motivated by developments in AG. I imagine one could write books on the subject, but probably the first moment one encounters homological algebra in algebraic geometry is the following.
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One needs a substantial amount of admittedly, not very deep, but that depends on who you are talking to This is all nicely explained in the standard textbook by R. Sign up to join this community. The best answers are voted up and rise to the top.
Home Questions Tags Users Unanswered. Homological methods in algebraic geometry Ask Question. Asked 5 years, 9 months ago.
Advanced Algebra: Homological Algebra
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Alexander Grothendieck. Alexander Grothendieck Alexander Grothendieck 1, 11 11 silver badges 32 32 bronze badges. The right derived functors of the global sections of a sheaf are what are known as the sheaf cohomology.
These are useful, for example, in understanding invariants of line bundles on projective varieties.