Year: 2026
Type: preprint
Abstract: We first establish estimates for the projective and injective dimensions for quotients of perfectoid algebras by radical ideals. As applications, we obtain homological characterizations of modules of finite injective dimension, (big) Cohen--Macaulay modules, Gorenstein local rings, and regular local rings in mixed characteristic in terms of perfectoid algebras. These are mixed characteristic analogues of the corresponding characterizations via Frobenius morphisms in positive characteristic.
Source: arXiv (Cornell University)
Authors: Asgharzadeh, Mohsen, Ishizuka, Ryo
Institution: Institute of Science Tokyo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169855536