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arXiv · 2403.13637

DG singular equivalence and singular locus

Leilei Liu·Jieheng Zeng
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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 $X \rightarrow \mathrm{Spec}(R /I)$, where $\mathrm{Spec}(R /I)$ is the singular locus in $\mathrm{Spec}(R)$. 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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Leilei Liu, Jieheng Zeng. 2024-03-20. DG singular equivalence and singular locus. https://arxiv.org/abs/2403.13637

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