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Derived Categories

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Author(s): Amnon Yekutieli
Series: Cambridge Studies in Advanced Mathematics 183
Publisher: Cambridge University Press
Year: 2019

Language: English
Pages: 608

Contents......Page 7
0 - Introduction......Page 13
1 - Basic Facts on Categories......Page 38
2 - Abelian Categories and Additive Functors......Page 49
3 - Differential Graded Algebra......Page 74
4 - Translations and Standard Triangles......Page 113
5 - Triangulated Categories and Functors......Page 129
6 - Localization of Categories......Page 158
7 - The Derived Category D(A,M......Page 177
8 - Derived Functors......Page 198
9 - DG and Triangulated Bifunctors......Page 228
10 - Resolving Subcategories of K(A,M)......Page 242
11 - Existence of Resolutions......Page 254
12 - Adjunctions, Equivalences and Cohomological Dimension......Page 301
13 - Dualizing Complexes over Commutative Rings......Page 342
14 - Perfect and Tilting DG Modules over NC DG Rings......Page 385
15 - Algebraically Graded Noncommutative Rings......Page 436
16 - Derived Torsion over NC Graded Rings......Page 474
17 - Balanced Dualizing Complexes over NC Graded Rings......Page 520
18 - Rigid Noncommutative Dualizing Complexes......Page 554
References......Page 602
Index......Page 612