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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.

MSC:
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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