PreprintCC BY 4.0arXiv
A blowup criterion for regularity
Abstract
We prove that a Noetherian integral domain is regular if, and only if, the derived pushforward of the structure sheaf along every blowup is a perfect complex. For suitable local rings, we give a construction which realizes a shift of the residue field as a direct summand of the derived pushforward of the structure sheaf along an explicit blowup.
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BibTeX
@misc{lank2026blowup,
title = {{A blowup criterion for regularity}},
author = {Pat Lank},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15691},
eprint = {2609.15691},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15691},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A blowup criterion for regularity
AU - Pat Lank
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15691
UR - https://arxiv.org/abs/2609.15691
AB - We prove that a Noetherian integral domain is regular if, and only if, the derived pushforward of the structure sheaf along every blowup is a perfect complex. For suitable local rings, we give a construction which realizes a shift of the residue field as a direct summand of the derived pushforward of the structure sheaf along an explicit blowup.
ER -