A local-global correspondence for perfectoid purity
Algebraic Geometry
2026-05-12 v2 Commutative Algebra
Number Theory
Abstract
We introduce (lim-)perfectoid splitting, which is a global variant of (lim-)perfectoid purity. Our main result establishes a correspondence between the lim-perfectoid splitting of projective schemes and the lim-perfectoid purity of their Gorenstein section rings. As an application, we construct a new supply of examples of lim-perfectoid pure rings that go beyond the previously known complete intersection or splinter-type cases.
Keywords
Cite
@article{arxiv.2604.25265,
title = {A local-global correspondence for perfectoid purity},
author = {Ryo Ishizuka and Shou Yoshikawa},
journal= {arXiv preprint arXiv:2604.25265},
year = {2026}
}
Comments
41 pages; minor change