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arXiv · 1006.2723

Smoothness of the truncated display functor

Eike Lau
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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 Dieudonne 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 Dieudonne modules over perfect rings.

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Eike Lau. 2010-06-14. Smoothness of the truncated display functor. https://arxiv.org/abs/1006.2723

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