Formal completions and idempotent completions of triangulated categories of singularities

Formal Completions and Idempotent Completions of Triangulated Categories of Singularities

The main goal of this paper is to prove that the idempotent completions of the triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic. We also discuss Thomason theorem on dense subcategories and a relation to the negative K-theory.

Cotopological completions and hulls of concrete categories

Extending valuations to formal completions

1 Introduction This paper is an extended version of the talk given by Miguel Olalla at the International Conference on Valuation Theory in El Escorial in July 2011. Its purpose is to provide an introduction to our joint paper [7] without grinding through all of its technical details. We refer the reader to [7] for details and proofs; only a few proofs are given in the present paper. Notation. T...

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...

Triangulated Categories of Gorenstein Cyclic Quotient Singularities

We prove there is an equivalence of derived categories between Orlov’s triangulated category of singularities for a Gorenstein cyclic quotient singularity and the derived category of representations of a quiver with relations, which is obtained from a McKay quiver by removing one vertex and half of the arrows. This result produces examples of distinct quivers with relations which have equivalen...