On the structure of dg categories of relative singularities

2019/11/04 by Pippi, Massimo
#14B05 #18G80 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.01332

Abstract

In this paper we show that every object in the dg category of relative singularities Sing(B,\underlinef) associated to a pair (B,\underlinef), where B is a ring and \underlinef∈ Bⁿ, is equivalent to a retract of a K(B,\underlinef)-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.

Related

• Relative singularity categories II: DG models
• Models for singularity categories
• Classifying dg-categories of matrix factorizations
• Differential graded enhancements of singularity categories
• Motivic Realizations of Singularity Categories and Vanishing Cycles