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Journal of the American Mathematical Society
Journal of the American Mathematical Society
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
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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Additional Information

Eike Lau
Affiliation: Institut für Mathematik, Universität Paderborn, D-33098 Paderborn, Germany
Email: elau@math.upb.de

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00744-9
PII: S 0894-0347(2012)00744-9
Received by editor(s): September 5, 2011
Received by editor(s) in revised form: May 25, 2012
Published electronically: June 28, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.