Derived categories / Amnon Yekutieli.
- Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.
- Cambridge studies in advanced mathematics; 183.
Cambridge studies in advanced mathematics ; 183
xi, 607 pages ; 24 cm.
- Derived categories (Mathematics)
- "There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important part (or component) of homological algebra. It carefully explains the foundations in detail before moving on to key applications in commutative and noncommutative algebra, many otherwise unavailable outside of research articles. These include commutative and noncommutative dualizing complexes, perfect DG modules, and tilting DG bimodules. Written with graduate students in mind, the emphasis here is on explicit constructions (with many examples and exercises) as opposed to axiomatics, with the goal of demystifying this difficult subject. Beyond serving as a thorough introduction for students, it will serve as an important reference for researchers in algebra, geometry and mathematical physics"-- Provided by publisher.
- Basic facts on categories
Abelian categories and additive functors
Differential graded algebra
Translations and standard triangles
Triangulated categories and functors
Localization of categories
The derived category D(A, M)
DG and triangulated bifunctors
Resolving subcategories of K(A, M)
Existence of resolutions
Adjunctions, equivalences and cohomological dimension
Dualizing complexes over commutative rings
Perfect and tilting DG modules over NC DG rings
Algebraically graded noncommutative rings
Derived torsion over NC graded rings
Balanced dualizing complexes over NC graded rings
Rigid noncommutative dualizing complexes.
- Includes bibliographical references and index.
- Other format:
- Online version: Yekutieli, Amnon. Derived categories.
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