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Derived categories of coherent sheaves

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arxiv math/0206295 v1 pith:IGOKSNSA submitted 2002-06-27 math.AG math.CT

Alexei Bondal , Dmitri Orlov This is my paper · ORCID
classification math.AGmath.CT
keywords categoriesbridgesderivedacrossalgebraicappeararchesbanks
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We show how derived categories build bridges across the current mathematical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal decompositions of triangulated categories. To appear in the Proceedings of the ICM 2002 in Beijing.

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  1. Categorical resolutions of cuspidal singularities

    math.AG 2024-11 conditional novelty 6.0 of 10

    A crepant categorical resolution of an isolated A2 singularity is shown to be a Verdier localization, with kernel generated by two 2-spherical objects (even dimension) or one non-spherical object (odd), and for cuspid...

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