On Some Permanence Properties of (Derived) Splinters

Abstract

We show that noetherian splinters ascend under essentially étale homomorphisms. Along the way, we also prove that the henselization of a noetherian local splinter is always a splinter and that the completion of a local splinter with geometrically regular formal fibers is a splinter. Finally, we give an example of a (nonexcellent) Gorenstein local splinter with mild singularities whose completion is not a splinter. Our results provide evidence for a strengthening of the direct summand theorem, namely that regular maps preserve the splinter property.