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Dieudonné theory over semiperfect rings and perfectoid rings

Part of: (Co)homology theory Algebraic groups

Published online by Cambridge University Press:  17 August 2018

Eike Lau
Eike Lau*
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany email lau@math-uni-bielefeld.de
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Abstract

The Dieudonné crystal of a $p$-divisible group over a semiperfect ring $R$ can be endowed with a window structure. If $R$ satisfies a boundedness condition, this construction gives an equivalence of categories. As an application we obtain a classification of $p$-divisible groups and commutative finite locally free $p$-group schemes over perfectoid rings by Breuil–Kisin–Fargues modules if $p\geqslant 3$.

MSC classification

Primary: 14L05: Formal groups, $p$-divisible groups
Secondary: 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 9 , September 2018 , pp. 1974 - 2004
Copyright
© The Author 2018 

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