Deformation theory of objects in homotopy and derived categories. I: General theory
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Publication:838129
DOI10.1016/j.aim.2009.03.021zbMath1180.18006arXivmath/0702838OpenAlexW2038773140MaRDI QIDQ838129
Dmitri O. Orlov, Alexander I. Efimov, Valery A. Lunts
Publication date: 21 August 2009
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0702838
Module categories in associative algebras (16D90) Resolutions; derived functors (category-theoretic aspects) (18G10) Abstract and axiomatic homotopy theory in algebraic topology (55U35)
Related Items (16)
Derived, coderived, and contraderived categories of locally presentable abelian categories ⋮ Non-commutative derived moduli prestacks ⋮ Gopakumar-Vafa invariants and wall-crossing ⋮ Deformation theory of objects in homotopy and derived categories. III: Abelian categories ⋮ Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration ⋮ Three notions of dimension for triangulated categories ⋮ Thick subcategories on curves ⋮ On non-commutative formal deformations of coherent sheaves on an algebraic variety ⋮ Deformation theory of objects in homotopy and derived categories. II: Pro-representability of the deformation functor ⋮ Uniqueness of enhancement for triangulated categories ⋮ Noncommutative deformations and flops ⋮ DIFFERENTIAL GRADED ENDOMORPHISM ALGEBRAS, COHOMOLOGY RINGS AND DERIVED EQUIVALENCES ⋮ Rational equivalence and Lagrangian tori on K3 surfaces ⋮ Proper connective differential graded algebras and their geometric realizations ⋮ The derived deformation theory of a point ⋮ Non-commutative thickening of moduli spaces of stable sheaves
Cites Work
- Deformation theory of objects in homotopy and derived categories. III: Abelian categories
- Deformation theory of objects in homotopy and derived categories. II: Pro-representability of the deformation functor
- Koszul duality for operads
- DG quotients of DG categories.
- Noncommutative deformations of modules
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- A Darboux theorem for Hamiltonian operators in the formal calculus of variations.
- Lie theory for nilpotent \(L_{\infty}\)-algebras
- Derived quot schemes
- ENHANCED TRIANGULATED CATEGORIES
- Deriving DG categories
- Derived Hilbert schemes
- Obstruction Theory for Objects in Abelian and Derived Categories
- The deformation theory of representations of fundamental groups of compact Kähler manifolds
- DG coalgebras as formal stacks
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