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Derived Category Methods in Commutative Algebra

Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck’s Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers...

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Bibliographic Details
Main Authors: Christensen, Lars Winther (Author), Foxby, Hans-Bjørn (Author), Holm, Henrik (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
Edition:1st ed. 2024.
Series:Springer Monographs in Mathematics,
Subjects:
Algebra, Homological.
Commutative algebra.
Commutative rings.
Category Theory, Homological Algebra.
Commutative Rings and Algebras.
Online Access:https://doi.org/10.1007/978-3-031-77453-9
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Table of Contents:
  • 1 Modules
  • 2 Complexes
  • 3 Categorical Constructions
  • 4 Equivalences and Isomorphisms
  • 5 Resolutions
  • 6 The Derived Category
  • 7 Derived Functors
  • 8 Homological Dimensions
  • 9 Gorenstein Homological Dimensions
  • 10 Dualizing Complexes
  • 11 Torsion and Completion
  • 12 A Brief for Commutative Ring Theorists
  • 13 Derived Torsion and Completion
  • 14 Krull Dimension, Depth, and Width
  • 15 Support Theories
  • 16 Homological Invariants over Local Rings
  • 17 Going Local
  • 18 Dualities and Cohen-Macaulay Rings
  • 19 Gorenstein Dimensions and Gorenstein Rings
  • 20 Global Dimension and Regular Rings
  • APPENDIX A: Acyclicity and Boundedness
  • APPENDIX B: Minimality
  • APPENDIX C: Structure of Injective Modules
  • APPENDIX D: Projective Dimension of Flat Modules
  • APPENDIX E: Triangulated Categories.

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