Derived categories

Research output: Book/ReportBookpeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish
Place of PublicationCambridge, United Kingdom
PublisherCambridge University Press
Number of pages608
ISBN (Electronic)9781108292825
ISBN (Print)9781108419338
DOIs
StatePublished - 1 Jan 2019

Publication series

NameCambridge studies in advanced mathematics
PublisherCambridge University Press
Volume183

ASJC Scopus subject areas

  • Mathematics (all)

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