Derived equivalences by quantization

2005/04/28 by Kaledin, D. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0504584

Abstract

We assume given a smooth symplectic (in the algebraic sense) resolution X of an affine algebraic variety Y, and we prove that, possibly after replacing Y with an etale neighborhood of a point, the derived category of coherent sheaves on X is equivalent to the dervied category of finitely generated left modules over a non-commutative algebra R, a non-commutative resolution of Y in a sense close to that of M. Van den Bergh. We also prove some applications, such as: two resolutions are derived-equivalent; every resolution X admits a "resolution of the diagonal"; the cohomology groups of the fibers of the map X → Y are spanned by fundamental classes of algebraic cycles.

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• Perverse coherent sheaves on symplectic singularities

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