$\delta$-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Commutative Algebra
2025-09-16 v2 Algebraic Geometry
Number Theory
Abstract
The aim of this article is to study basic structures and interrelations of -rings, perfectoid towers, and lim Cohen-Macaulay sequences over Noetherian rings in positive or mixed characteristic. Then we discuss some methods for constructing perfectoid towers, dealing with -torsion free and -torsion cases, respectively. Some interesting examples arise as quotients by monomial or binomial ideals or determinantal rings. We also explain a geometric method with a view toward constructing rings with certain singularities.
Keywords
Cite
@article{arxiv.2509.06527,
title = {$\delta$-rings, perfectoid towers, and lim Cohen-Macaulay sequences},
author = {Shinnosuke Ishiro and Kazuma Shimomoto},
journal= {arXiv preprint arXiv:2509.06527},
year = {2025}
}
Comments
31 pages, v2:remove the condition of (ii) in Theorem 4.6, and revised Example 4.9 and Corollary 4.10