Classification of objects in the singularity categories of rational double points in arbitrary characteristics

We study rational double points over algebraically closed fields in arbitrary characteristics and completely classify the indecomposable objects in their singularity categories, which correspond to the vertices in their Auslander-Reiten quivers. Along the way, we present an alternative proof determining the configuration of these Auslander-Reiten quivers, and provide methods to handle the homotopy categories of matrix factorizations of isolated hypersurface singularities with computer algebra systems.