Smoothness of the truncated display functor

Lau, Eike

doi:10.1090/S0894-0347-2012-00744-9

Smoothness of the truncated display functor
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by Eike Lau

J. Amer. Math. Soc. 26 (2013), 129-165

DOI: https://doi.org/10.1090/S0894-0347-2012-00744-9

Published electronically: June 28, 2012

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Abstract:

We show that to every $p$-divisible group over a $p$-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 $p$-divisible groups and nilpotent displays over $p$-adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of $p$-power order and Dieudonné modules over perfect rings.

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