Categorical resolution of singularities

2009/05/28 by Valery A. Lunts, Lunts, Valery A. · 4 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0905.4566

openalex publication_date 2009/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Building on the concept of a smooth DG algebra we define the notion of a smooth derived category. We the propose the definition of a categorical resolution of singularities. Our main example is the derived category D(X) of quasi-coherent sheaves on a scheme X. We prove that D(X) has a canonical categorical resolution if the base field is perfect and X is a separated scheme of finite type with a dualizing complex.

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