Purity in categories of sheaves

Derived Categories Of Sheaves

4 Derived Tensor 15 4.1 Tensor Product of Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Hoflat Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Derived Tensor Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Change of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and triangulated category of singularities of the fiber of W over zero. We also proved that the category of graded D-branes of type B in such LG-models is connected by a fully faithful functor with the derived category of coherent sheaves on the...

Explicit Methods for Derived Categories of Sheaves

These notes aim to complement the lecture notes of Căldăraru by providing an introduction to explicit methods in the study of derived categories in algebraic geometry. The bounded derived category of coherent sheaves on certain very simple algebraic varieties is equivalent to the bounded derived category of finitely generated modules over an algebra. We provide an introduction to this circle of...

Derived Categories of Coherent Sheaves and Motives

The bounded derived category of coherent sheaves D(X) is a natural triangulated category which can be associated with an algebraic variety X. It happens sometimes that two different varieties have equivalent derived categories of coherent sheaves D(X) ≃ D(Y ). There arises a natural question: can one say anything about motives of X and Y in that case? The first such example (see [4]) – abelian ...

Structure sheaves of definable additive categories