Perfectoid towers generated from prisms

TL;DR

This paper introduces a unified method to construct perfectoid towers from prisms, enabling systematic creation for a broad class of rings with Frobenius lift, including all Frobenius liftings of reduced _p-algebras.

Contribution

It provides a general construction framework that encompasses all previous perfectoid tower constructions from prisms, broadening applicability.

Findings

Unified construction covers all previous perfectoid towers from prisms.

Any Frobenius lift of a reduced _p-algebra admits a perfectoid tower.

Systematic method applicable to a large class of rings with Frobenius lift.

Abstract

We present a unified construction of perfectoid towers from specific prisms which covers all the previous constructions of (p-torsion-free) perfectoid towers. By virtue of the construction, perfectoid towers can be systematically constructed for a large class of rings with Frobenius lift. Especially, any Frobenius lifting of a reduced $\mathbb{F}_p$-algebra has a perfectoid tower.