We consider (big) singularity categories and Gorenstein defect categories in the setting of exact categories, and especially in the presence of a complete hereditary cotorsion pair. As a main result, we show that the vanishing of this more general Gorenstein defect category characterizes finiteness of certain Gorenstein dimensions and provide an equivalence of a big singularity category with the stable category of Gorenstein objects. Applications include a viable non-affine analogue of the (big) singularity category of a ring and a perspective on the finitistic dimension conjecture.
This talk was part of the one-day meeting Triangulated Categories in Representation Theory, which took place online in 2021.
