Subcategories of triangulated categories and the smashing conjecture / Kristian Brüning. 2007
Content
- Contents
- Introduction
- Triangulated categories and their localization
- Definitions and examples
- Thick subcategories and Verdier-quotients
- Localizations
- Smashing and finite localizations
- The Telescope Conjecture and the Smashing Conjecture
- The Telescope Conjecture in stable homotopy theory
- The Smashing Conjecture in commutative algebra
- Keller's counterexample
- The Smashing Conjecture for stable module categories
- The Smashing Conjecture for arbitrary triangulated categories
- Applications
- Cotorsion pairs, model categories and finite generation
- Realizing smashing localizations of differential graded algebras
- Differential graded algebras
- Cofibrant differential graded algebras
- Cohomological p-Localization
- Smashing localizations of the derived category of a dg algebra
- Smashing subcategories of algebraic triangulated categories
- The p-localization of a dg algebra
- Thick subcategories of the derived category of a hereditary algebra
- Representation theory of hereditary algebras of finite representation type
- The derived category of hereditary abelian categories
- Thick subcategories of abelian categories
- Classification of thick subcategories
- Classification of localizing subcategories
- References