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

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.

arXiv comment15 pages, final version, to appear in Mathematical Research Letters