Derived Categories
Localization at quasi-isomorphisms and triangulated structure.
Derived Categories. Localization at quasi-isomorphisms and triangulated structure.
Foundations and canonical references
The standard treatments of derived categories approach the subject from complementary angles. Gelfand, Methods of Homological Algebra (2003) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Kashiwara, Sheaves on Manifolds (1990) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for derived categories include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2003Methods of Homological Algebragelfand-2003, manin-2003
- textbook · primary · 1990Sheaves on Manifoldskashiwara-1990, schapira-1990
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