Categorical resolution of singularities

Abstract

Building on the concept of a smooth DG algebra we define the notion of a smooth derived category. We the propose the definition of a categorical resolution of singularities. Our main example is the derived category $D(X)$ of quasi-coherent sheaves on a scheme $X$. We prove that $D(X)$ has a canonical categorical resolution if the base field is perfect and $X$ is a separated scheme of finite type with a dualizing complex.

The previous version with the same title is split into two parts. This is the first part

References in corpus (1)

• Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor

Cited by in corpus (1)

• Thom-Sebastiani & Duality for Matrix Factorizations