Homological theory of k-idempotent ideals in dualizing varieties

Abstract

In this work, we develop the theory of k-idempotent ideals in the setting of dualizing varieties. Several results given previously by Auslander et al. are extended to this context. Given an ideal (which is the trace of a projective module), we construct a canonical recollement which is the analog to a well-known recollement in categories of modules over artin algebras. Moreover, we study the homological properties of the categories involved in such a recollement. Consequently, we find conditions on the ideal to obtain quasi-hereditary algebras in such a recollement. Applications to bounded derived categories are also given.