Triangulated Categories

doi:10.1017/CBO9781139107075

Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. These self-contained articles are a useful introduction for graduate students entering the field and a valuable reference for experts.

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Triangulated Categories

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Triangulated categories: definitions, properties, and examples
pp 1-51

Cohomology over complete intersections via exterior algebras
pp 52-75

Cluster algebras, quiver representations and triangulated categories
pp 76-160

Localization theory for triangulated categories
pp 161-235

Homological algebra in bivariant K-theory and other triangulated categories. I
pp 236-289

Derived categories and Grothendieck duality
pp 290-350

Derived categories and algebraic geometry
pp 351-370

Triangulated categories for the analysts
pp 371-388

Algebraic versus topological triangulated categories
pp 389-407

Derived categories of coherent sheaves on algebraic varieties
pp 408-451

Rigid dualizing complexes via differential graded algebras (survey)
pp 452-463

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Triangulated Categories

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