Tuesday, July 15, 14:00, 7.527

Hanno Becker (Bonn),
Models for singularity categories, I and II.

Abstract:
In this talk I will introduce localizations of abelian model structures and use them to construct models for the singularity categories of differential graded rings. The interplay between these singular model structures and the classical model structures allows for a lift of Krause's recollement (connecting the singularity category, the ordinary derived category, and Positselski's coderived category) to the level of model categories. After that, I will discuss the special case of Gorenstein rings and hypersurface singularites, connecting the above models to known models in terms of Gorenstein projective modules and matrix factorizations. Finally, we will consider the main technical ingredient in the construction of the singular model structures, namely the stability of deconstructible classes under pullback along monadic functors.