Theorie homotopique des DG-categories

Abstract

In this thesis we present several original contributions to the study of: - DG categories and their invariants; - Neeman's well-generated (algebraic) triangulated categories; - Fomin-Zelevinsky's cluster algebras approach via representation theory.

In french and english; 178 pages

References in corpus (4)

• On triangulated orbit categories
• Calabi-Yau algebras
• Semiorthogonal decomposition for algebraic varieties
• Failure of Brown representability in derived categories

Cited by in corpus (18)

• Uniqueness of enhancement for triangulated categories
• Smooth and proper noncommutative schemes and gluing of DG categories
• Duality between Lagrangian and Legendrian invariants
• Two-dimensional categorified Hall algebras
• The nonequivariant coherent-constructible correspondence for toric stacks
• Topological Hochschild and cyclic homology for Differential graded categories
• Morita cohomology
• Finite-dimensional differential graded algebras and their geometric realizations
• Orlov and Viterbo functors in partially wrapped Fukaya categories
• Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
• Categorical Koszul duality
• Higher nonunital Quillen K'-theory, KK-dualities and applications to topological $\mathbb{T}$-dualities
• Homotopy theory of Spectral categories
• On the derived category of ${\bar{M}}_{0,n}$
• The fundamental isomorphism conjecture via non-commutative motives
• Noncommutative Geometry in the Framework of Differential Graded Categories
• Noncommutative correspondence categories, simplicial sets and pro $C^{\ast }$-algebras
• Rational homotopy theory and differential graded category