Abstract: Let A be a differential bigraded k-algebra and let e be an idempotent of A. Under suitable assumptions on the pair (A,e), we define the graded Higgs category H and the graded relative cluster category C. We show that H carries a Frobenius extriangulated structure, and that its stable category admits a silting object. Examples arise from Keller-Scherotzke's work on graded singular Nakajima categories and from graded maximal Cohen-Macaulay modules over isolated singularities. This is a report on ongoing joint work with Li Fan.
This talk will take place in hybrid mode at the Institut Henri Poincaré.