This note is an expansion of a talk I gave at ICRA 2020. We consider the smallest triangulated subcategory of the derived category of a ring that contains the injective modules and is closed under infinite coproducts. When this subcategory is the entire derived category, we say that injectives generate for the ring. For rings that appear in recollements we ask, if injectives generate for some of the rings, do injectives generate for the other rings, and vice versa?

Recollements and injective generation of the derived category

Charley Cummings

Abstract