Smoothness of the truncated display functor

We show that to every pp-divisible group over a pp-adic ring one can associate a display by crystalline Dieudonné theory. For an appropriate notion of truncated displays, this induces a functor from truncated Barsotti-Tate groups to truncated displays, which is a smooth morphism of smooth algebraic...

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Bibliographic Details
Published in:Journal of the American Mathematical Society 2013-01, Vol.26 (1), p.129-165
Main Author: Lau, Eike
Format: Article
Language:English
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Research article
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Summary:We show that to every pp-divisible group over a pp-adic ring one can associate a display by crystalline Dieudonné theory. For an appropriate notion of truncated displays, this induces a functor from truncated Barsotti-Tate groups to truncated displays, which is a smooth morphism of smooth algebraic stacks. As an application we obtain a new proof of the equivalence between infinitesimal pp-divisible groups and nilpotent displays over pp-adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of pp-power order and Dieudonné modules over perfect rings.
ISSN:0894-0347
1088-6834
DOI:10.1090/S0894-0347-2012-00744-9