Applications of resolving subcategories to singularity categories and monomorphism categories

This is the authors' abstract. We don't add key points for this paper.

In this paper, we study resolving subcategories and singularity categories. First, if the left perpendicular category of a module [Formula: see text] over an Artin algebra [Formula: see text] is the additive closure of another module [Formula: see text], then the singularity category of [Formula: see text] and that of the endomorphism algebra [Formula: see text] of [Formula: see text] are closed related. This gives a categorical version of a recent result of Zhang ( [31, Theorem 2]). Second, we apply the resolution theorem for derived categories to elliptic curves, the monomorphism subcategory of a Gorenstein algebra and of a kind of Eilenberg–Moore category. As consequences, their singularity categories are equivalent, which explains why monomorphism categories are closely related to singularity categories.