Categorical resolution of singularities

Details Categorical resolution of singularities Categorical resolution of singularities

2009-05-28

arxiv.org/abs/0905.4566v3

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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