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Mosc. Math. J., 2002, Volume 2, Number 2, Pages 249–279 (Mi mmj55)  

This article is cited in 23 scientific papers (total in 23 papers)

Group schemes with strict $\mathcal{O}$-action

G. Faltings

Max Planck Institute for Mathematics

Abstract: Let $\mathcal{O}$ denote the ring of integers in a $p$-adic local field. Recall that $\mathcal{O}$-modules are formal groups with an $\mathcal{O}$-action such that the induced action on the Lie algebra is via scalars. In the paper this notion is generalised to finite flat group schemes. It is shown that the usual properties carry over. For example, Cartier duality holds with the multiplicative group replaced by the Lubin–Tate group. We also show that liftings over $\mathcal{O}$-divided powers are controlled by Dieudonné modules or, better, by complexes. For these facts new proofs have to be invented, because the classical recipe of embedding into abelian varieties is not available.

Key words and phrases: Finite flat group schemes, Lubin–Tate groups, $\mathcal{O}$-modules.


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MSC: 14L15
Received: February 18, 2002; in revised form May 28, 2002

Citation: G. Faltings, “Group schemes with strict $\mathcal{O}$-action”, Mosc. Math. J., 2:2 (2002), 249–279

Citation in format AMSBIB
\by G.~Faltings
\paper Group schemes with strict $\mathcal{O}$-action
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 2
\pages 249--279

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    3. Strauch M., “Deformation spaces of one-dimensional formal modules and their cohomology”, Advances in Mathematics, 217:3 (2008), 889–951  crossref  mathscinet  zmath  isi
    4. Hartl U., “A dictionary between Fontaine-Theory and its analogue in equal characteristic”, Journal of Number Theory, 129:7 (2009), 1734–1757  crossref  mathscinet  zmath  isi
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