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 …

We show how derived categories build bridges across the current mathematical mainstream,
linking geometric and algebraic, commutative and noncommutative, local and global banks …

The paper contains general results on the uniqueness of a DG enhancement for triangulated
categories. As a consequence we obtain such uniqueness for the unbounded derived …

We consider a semi-abelian category V and we write Act (G, X) for the set of actions of the
object G on the object X, in the sense of the theory of semi-direct products in V. We …

This is the first in a series of papers that deals with duality statements such as Mukai-duality
(T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $ K …

In this paper we study the category of standard holomorphic vector bundles on a
noncommutative two-torus. We construct a functor from the derived category of such bundles …

In this paper we discuss different properties of noncommutative schemes over a field. We
define a noncommutative scheme as a differential graded category of a special type. We …

We introduce relative noncommutative Calabi–Yau structures defined on functors of
differential graded categories. Examples arise in various contexts such as topology …

arXiv:0804.1163v2 [math.AG] 16 Apr 2008 Page 1 arXiv:0804.1163v2 [math.AG] 16 Apr
2008 REMARKS ON GENERATORS AND DIMENSIONS OF TRIANGULATED …

We consider the abelian group PT generated by quasi-equivalence classes of
pretriangulated DG categories with relations coming from semiorthogonal decompositions of …