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"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 part (or component) of homological algebra. It carefully explains the...
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| Main Authors: | |
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| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge : |
| Publication Dates: | 2020. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge studies in advanced mathematics ;
183 |
| Subjects: | |
| Summary: |
"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 part (or 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 i |
| Carrier Form: | xi, 607 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 590-599) and index. |
| ISBN: |
9781108419338 (hardback) : 110841933X (hardback) 9781108292825 (epub) 1108292828 (epub) |
| Index Number: | QA169 |
| CLC: | O154.1 |
| Call Number: | O154.1/Y436 |
| Contents: | Basic facts on categories -- Abelian categories and additive functors -- Differential graded algebra -- Translations and standard triangles -- Triangulated categories and functors -- Localization of categories -- The derived category D(A, M) -- Derived functors -- DG and triangulated bifunctors -- Resolving subcategories of K(A, M) -- Existence of resolutions -- Adjunctions, equivalences and cohomological dimension -- Dualizing complexes over commutative rings -- Perfect and tilting DG modules over NC DG rings -- Algebraically graded noncommutative rings -- Derived torsion over NC graded rin |