$p$-complete arc-descent for perfect complexes over integral perfectoid rings

TL;DR

This paper establishes $p$-complete arc-descent for perfect complexes over integral perfectoid rings, aiding the classification of $p$-divisible groups and advancing understanding in perfectoid geometry.

Contribution

It proves $p$-complete arc-descent for perfect complexes over integral perfectoid rings, providing a key reduction in classifying $p$-divisible groups.

Findings

Proves $p$-complete arc-descent for finite projective modules.

Clarifies a reduction step in classifying $p$-divisible groups.

Enhances techniques in perfectoid ring theory.

Abstract

We prove $p$-complete arc-descent results for finite projective modules and perfect complexes over integral perfectoid rings. Using our results, we clarify a reduction argument in the proof of the classification of $p$-divisible groups over integral perfectoid rings given by Scholze-Weinstein.