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The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.
List of contents
Introduction; 1. Basic facts on categories; 2. Abelian categories and additive functors; 3. Differential graded algebra; 4. Translations and standard triangles; 5. Triangulated categories and functors; 6. Localization of categories; 7. The derived category D(A,M); 8. Derived functors; 9. DG and triangulated bifunctors; 10. Resolving subcategories of K(A,M); 11. Existence of resolutions; 12. Adjunctions, equivalences and cohomological dimension; 13. Dualizing complexes over commutative rings; 14. Perfect and tilting DG modules over NC DG rings; 15. Algebraically graded noncommutative rings; 16. Derived torsion over NC graded rings; 17. Balanced dualizing complexes over NC graded rings; 18. Rigid noncommutative dualizing complexes; References; Index.
About the author
Amnon Yekutieli is Professor of Mathematics at Ben-Gurion University of the Negev, Israel. His research interests are in algebraic geometry, ring theory, derived categories and deformation quantization. He has taught several graduate-level courses on derived categories and has published three previous books.
Summary
This book is the first systematic exposition of the theory of derived categories. It carefully explains the foundations before moving on to key applications in (non)commutative algebra, including derived categories of DG modules. Many examples and exercises serve to demystify this difficult but important part of modern homological algebra.
