Séminaires : Séminaire d'Algèbre

In 2018, Kalck and Yang showed that the singularity categories associated with 3-dimensional Gorenstein quotient singularities are triangle equivalent (up to direct summands) to small cluster categories associated with McKay quivers with potential. I introduce graded McKay quivers with potential and generalize Kalck-Yang's theorem to arbitrary dimensions. The singularity categories I consider occur as stable categories of categories of maximal Cohen-Macaulay modules. I refine my description of the singularity categories by showing that these categories of maximal Cohen-Macaulay modules are equivalent to Higgs categories in the sense of Wu. Moreover, I describe the singularity categories in the non-Gorenstein case. 

This talk will take place on Zoom only.