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Finite-dimensional differential graded algebras and their geometric realizations
Dmitri Orlov
We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the categ…
Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
Dmitri Orlov
The main purpose of this paper is to describe various phenomena and certain constructions arising in the process of studying derived noncommutative schemes. Derived noncommutative…
Equivariant exceptional collections on smooth toric stacks
Lev Borisov, Dmitri Orlov
We study the bounded derived categories of torus-equivariant coherent sheaves on smooth toric varieties and Deligne-Mumford stacks. We construct and describe full exceptional colle…
DG deformation theory of objects in homotopy and derived categories I
Valery A. Lunts, Dmitri Orlov
We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general pro-representability theorem for the correspond…