Year: 2026
Type: preprint
Abstract: Using André's lemma and the excision square for perfectoidization coming from $p$-complete arc descent, we prove new structural results about perfectoid rings and perfectoidization. The main result is a tameness theorem for torsion in perfectoid rings: if $R$ is a perfectoid ring and $I\subset R$ is an ideal, then the $I$-torsion in $R$ is $I_{\mathrm{perfd}}$-almost zero. This yields an excision-type decomposition of $R$ along its $I$-torsion part. We also study (semi)perfectoid rings and perfectoid ideals and take the opportunity to make some structural remarks about them.
Source: arXiv (Cornell University)
Authors: Ishizuka, Ryo, Chafloque, Léo Navarro
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163647143