Derived Categories

Erscheinungsjahr 2020
ISBN: 978-1-108-41933-8
Verlag: Cambridge University Press

Buch, Englisch, Band 183, 370 Seiten, Format (B × H): 159 mm x 234 mm, Gewicht: 1012 g

Reihe: Cambridge Studies in Advanced 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 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.

Autoren/Hrsg.

Yekutieli, Amnon

Inhaltsverzeichnis

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.

Über Autor(innen)

Yekutieli, Amnon
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.