Noncommutative resolutions and intersection cohomology for quotient\n singularities

2021/03/10 by Tudor Pădurariu, Pădurariu, Tudor · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2103.06215

openalex publication_date 2021/03/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

For a large class of good moduli spaces X of symmetric stacks\n\X, we define noncommutative motives mathbbD^\nc(X)\nwhich can be regarded as categorifications of the intersection cohomology of\nX. These motives are summands of noncommutative resolutions of singularities\n mathbbD(X)\⊂ D^b(\X) of X. The category mathbbD(X) is\na global analogue of the noncommutative resolutions of singularities of V//G\nfor V a symmetric representation of a reductive group G constructed by\n vSpenko-Van den Bergh.\n

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