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arXiv · 1911.01332

On the structure of dg categories of relative singularities

Massimo Pippi
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Abstract

In this paper we show that every object in the dg category of relative singularities Sing$(B,\underline{f})$ associated to a pair $(B,\underline{f})$, where $B$ is a ring and $\underline{f}\in B^n$, is equivalent to a retract of a $K(B,\underline{f})$-dg module concentrated in $n+1$ degrees. When $n=1$, we show that Orlov's comparison theorem, which relates the dg category of relative singularities and that of matrix factorizations of an LG-model, holds true without any regularity assumption on the potential.

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Massimo Pippi. 2019-11-04. On the structure of dg categories of relative singularities. https://arxiv.org/abs/1911.01332

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