Centers of perfectoid purity
Algebraic Geometry
2025-09-17 v2 Commutative Algebra
Abstract
We introduce a mixed characteristic analog of log canonical centers in characteristic and centers of -purity in positive characteristic, which we call centers of perfectoid purity. We show that their existence detects (the failure of) normality of the ring. We also show the existence of a special center of perfectoid purity that detects the perfectoid purity of , analogously to the splitting prime of Aberbach and Enescu, and investigate its behavior under \'etale morphisms.
Cite
@article{arxiv.2504.15569,
title = {Centers of perfectoid purity},
author = {Anne Fayolle},
journal= {arXiv preprint arXiv:2504.15569},
year = {2025}
}
Comments
Final version, published in Journal de l'\'Ecole polytechnique