Derived Categories
eBook - PDF

Derived Categories

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Derived Categories

About this book

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.

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Yes, you can access Derived Categories by Amnon Yekutieli in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Half-title
  3. Series information
  4. Title page
  5. Copyright information
  6. Dedication
  7. Contents
  8. 0 Introduction
  9. 1 Basic Facts on Categories
  10. 2 Abelian Categories and Additive Functors
  11. 3 Differential Graded Algebra
  12. 4 Translations and Standard Triangles
  13. 5 Triangulated Categories and Functors
  14. 6 Localization of Categories
  15. 7 The Derived Category D(A,M)
  16. 8 Derived Functors
  17. 9 DG and Triangulated Bifunctors
  18. 10 Resolving Subcategories of K(A,M)
  19. 11 Existence of Resolutions
  20. 12 Adjunctions, Equivalences and Cohomological Dimension
  21. 13 Dualizing Complexes over Commutative Rings
  22. 14 Perfect and Tilting DG Modules over NC DG Rings
  23. 15 Algebraically Graded Noncommutative Rings
  24. 16 Derived Torsion over NC Graded Rings
  25. 17 Balanced Dualizing Complexes over NC Graded Rings
  26. 18 Rigid Noncommutative Dualizing Complexes
  27. References
  28. Index