On Quasi-$F$-Purity of Excellent Rings
Commutative Algebra
2025-09-30 v2 Algebraic Geometry
Abstract
We introduce an analogue to Quasi--splittings, Quasi--purity, which is definable over rings that are not necessarily -finite. We show that this property is equivalent to being Quasi--split in the complete local and -finite case. We then exhibit that it is stable under completion, direct limit, and local/finite \'etale extension.
Keywords
Cite
@article{arxiv.2503.10778,
title = {On Quasi-$F$-Purity of Excellent Rings},
author = {Vignesh Jagathese},
journal= {arXiv preprint arXiv:2503.10778},
year = {2025}
}
Comments
Final version, to appear in Communications in Algebra LAGB