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TRUNCATED BARSOTTI–TATE GROUPS AND DISPLAYS

Part of: (Co)homology theory Algebraic groups

Published online by Cambridge University Press:  04 April 2016

Eike Lau  and
Thomas Zink
Eike Lau
Affiliation:
Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
Thomas Zink
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
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Abstract

We define truncated displays over rings in which a prime $p$ is nilpotent, we associate crystals to truncated displays, and we define functors from truncated displays to truncated Barsotti–Tate groups.

Keywords

p-divisible groupsdisplayscrystalline cohomology

MSC classification

Primary: 14L05: Formal groups, $p$-divisible groups 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 3 , June 2018 , pp. 541 - 581
Copyright
© Cambridge University Press 2016 

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References

Illusie, L., Deformations de groupes de Barsotti–Tate (d’après A. Grothendieck), in Seminar on Arithmetic Bundles: The Mordell Conjecture, Astérisque, Volume 127, pp. 151–198. (1985).Google Scholar
Lau, E., Displays and formal p-divisible groups, Invent. Math. 171 (2008), 617–628.Google Scholar
Lau, E., Smoothness of the truncated display functor, J. Amer. Math. Soc. 26 (2013), 129–165.Google Scholar
Lau, E., Relations between Dieudonné displays and crystalline Dieudonné theory, Algebra and Number Theory 8 (2014), 2201–2262.Google Scholar
Messing, W., The Crystals Associated to Barsotti–Tate Groups: With Applications to Abelian Schemes, Lecture Notes in Mathematics, Volume 264 (Springer, Berlin, Heidelberg, New York, 1972).Google Scholar
Milne, J., Étale Cohomology (Princeton University Press, Princeton, 1980).Google Scholar
Neeman, A., The derived category of an exact category, J. Algebra 135 (1990), 388–394.Google Scholar
Thomason, R. and Trobaugh, T., Higher algebraic K-theory of schemes and of derived categories, in The Grothendieck Festschrift, Vol. III, Progress in Mathematics, Volume 88, pp. 247–435 (Birkhäuser, Boston, 1990).Google Scholar
Zink, T., The display of a formal p-divisible group, Astérisque 278 (2002), 127–248.Google Scholar