• Publications
  • Influence
Semiorthogonal decompositions for algebraic varieties.
A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on theExpand
Generators and representability of functors in commutative and noncommutative geometry
We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces isExpand
REPRESENTATION OF ASSOCIATIVE ALGEBRAS AND COHERENT SHEAVES
It is proved that a triangulated category generated by a strong exceptional collection is equivalent to the derived category of modules over an algebra of homomorphisms of this collection. For theExpand
Reconstruction of a Variety from the Derived Category and Groups of Autoequivalences
We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We alsoExpand
Derived Categories of Coherent Sheaves
We show how derived categories build bridges across the current mathe­ matical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in theseExpand
HOMOLOGICAL PROPERTIES OF ASSOCIATIVE ALGEBRAS: THE METHOD OF HELICES
Homological properties of associative algebras arising in the theory of helices are studied. A class of noncommutative algebras is introduced in which it is natural (from the viewpoint of the theoryExpand
Ju n 20 02 Derived Categories of Coherent Sheaves
This paper is devoted to studying the derived categories Db(X) of coherent sheaves on smooth algebraic varieties X and on their noncommutative counterparts. Derived categories of coherent sheavesExpand
Theory of homotopes with applications to mutually unbiased bases, harmonic analysis on graphs, and perverse sheaves
This paper is a survey of contemporary results and applications of the theory of homotopes. The notion of a well-tempered element of an associative algebra is introduced, and it is proved that theExpand