PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{liu2026takahashis,
title = {{On Takahashi's descent question about dominant local rings}},
author = {Jian Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.14283},
eprint = {2608.14283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.14283},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Takahashi's descent question about dominant local rings
AU - Jian Liu
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2608.14283
UR - https://arxiv.org/abs/2608.14283
AB - 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.
ER -