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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. The most basic principle is to study the abelian category of quasi-coherent, resp.
As someone with only a cursory background in algebraic geometry, this certainly helped me understand a few of the motivations. Sign up or log in Sign up using Google.
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Related Hot Network Questions. Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse.
This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory sheaf cohomology, spectral sequences, etc. In most cases complete proofs are given.
Methods of Homological Algebra
Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections. It is based on the systematic use of the language and technics of derived categories and derived functors.
The reader has all the basic material and a lot of examples ….
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Related Methods of Homological Algebra
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