Smoothness of the truncated display functor

Lau, Eike

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

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ISSN 1088-6834(online) ISSN 0894-0347(print)

Smoothness of the truncated display functor

Author: Eike Lau
Journal: J. Amer. Math. Soc. 26 (2013), 129-165
MSC (2010): Primary 14F30, 14L05
Posted: June 28, 2012
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Abstract: We show that to every -divisible group over a -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 -divisible groups and nilpotent displays over -adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of -power order and Dieudonné modules over perfect rings.

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