DG singular equivalence and singular locus

2024/03/20 by Leilei Liu, Liu, Leilei, Jieheng Zeng +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2403.13637

openalex publication_date 2024/03/20 · openalex created_date 2024/03/22 · openalex updated_date 2026/07/28

Abstract

For a commutative Gorenstein Noetherian ring R, we construct an affine scheme X solely from DG singularity category S_dg(R) of R such that there is a finite surjective morphism X → Spec(R /I), where Spec(R /I) is the singular locus in Spec(R). As an application, for two such rings with equivalent DG singularity categories, we prove that the singular loci in their affine schemes have the same dimension.

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• Singular equivalence and the (Fg) condition