Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Liu, Jian
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2136804278
OpenAlex ID: W7203598968