ENGLISH

Derived Categories

By Amnon Yekutieli

Book information

Publisher
Cambridge University Press
Year
2020
ISBN
110841933X, 9781108419338
Language
english
Format
PDF
Filesize
2 MB (2293083 bytes)
Series
Cambridge Studies in Advanced Mathematics (Book 183)
Edition
1
Pages
370\622
Time added
2020-07-27 09:14:08

Description

This book is the first systematic exposition of the theory of derived categories. It carefully explains the foundations before moving on to key applications in (non)commutative algebra, including derived categories of DG modules. Many examples and exercises serve to demystify this difficult but important part of modern homological algebra. Cover Front Matter CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS Derived Categories Copyright Dedication Contents 0 Introduction 1 Basic Facts on Categories 2 Abelian Categories and Additive Functors 3 Differential Graded Algebra 4 Translations and Standard Triangles 5 Triangulated Categories and Functors 6 Localization of Categories 7 The Derived Category D(A;M) 8 Derived Functors 9 DG and Triangulated Bifunctors 10 Resolving Subcategories of K(A;M) 11 Existence of Resolutions 12 Adjunctions, Equivalences and Cohomological Dimension 13 Dualizing Complexes over Commutative Rings 14 Perfect and Tilting DG Modules over NC DG Rings 15 Algebraically Graded Noncommutative Rings 16 Derived Torsion over NC Graded Rings 17 Balanced Dualizing Complexes over NC Graded Rings 18 Rigid Noncommutative Dualizing Complexes References Index

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