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Categorical resolutions of irrational singularities. (English) Zbl 1338.14020
In this article, the authors show the existence of categorical resolutions of singularities over a field of characteristic zero. This means that the derived category of the singularity can be embedded fully and faithfully in to a smooth triangulated category that has a semiorthogonal decomposition with components equivalent to the derived categories of smooth varieties. Note that for rational singularities, the existence of a categorical resolution of singularities follows immediately from the usual resolution of singularities due to Hironaka.

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
18E30 Derived categories, triangulated categories (MSC2010)
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