On Takahashi's descent question about dominant local rings

Abstract

This article studies dominant local rings, a notion introduced by Takahashi. We prove that, for a flat local homomorphism R-->S between commutative noetherian local rings, dominance descends from S to R, thereby answering Takahashi's descent question affirmatively. The proof makes use of Krause's realization of the idempotent completion of the singularity category as the subcategory of compact objects in the homotopy category of acyclic complexes of injective modules.