Mathematical Research Letters

Volume 30 (2023)

Number 6

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

Pages: 1727 – 1749

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n6.a4

Author

Kazuhiro Ito (Mathematical Institute, Tohoku University, Sendai, Miyagi, Japan)

Abstract

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

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The work of the author was supported bythe European Research Council (ERC) under the European Union’s HorizonThe work of the author was supported bythe European Research Council (ERC) under the European Union’s Horizon2020 research and innovation programme (grant agreement No. 851146).

Received 2 January 2022

Received revised 3 May 2022

Accepted 29 May 2022

Published 17 July 2024