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Derived Category Methods in Commutative Algebra

Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm

Research output: Book/ReportBookResearchpeer-review

6 Citations (Scopus)

Abstract

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 familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings. The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.

Original languageEnglish
PublisherSpringer
Number of pages1,093
ISBN (Print) 978-3-031-77452-2
ISBN (Electronic)978-3-031-77453-9
DOIs
Publication statusPublished - 2024
SeriesSpringer Monographs in Mathematics
ISSN1439-7382

Bibliographical note

Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 .

Keywords

  • Cohen-Macaulay
  • Depth
  • Dualizing complex
  • Finitistic dimension
  • Global dimension
  • Gorenstein
  • Homological algebra
  • Homological dimension
  • Injective resolutions
  • Local cohomology
  • Local duality
  • Matlis duality
  • Projective resolutions
  • Unbounded derived category

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