Mathematical Research Letters

Volume 19 (2012)

Number 1

The classification of $p$-divisible groups over $2$-adic discrete valuation rings

Pages: 121 – 141

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n1.a10

Author

Wansu Kim (DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom)

Abstract

Let $\fo_K$ be a $2$-adic discrete valuation ring withperfect residue field $k$. We classify $p$-divisible groupsand $p$-power order finite flat group schemes over $\fo_K$in terms of certain Frobenius modules over$\Sig:=W(k)[[u]]$. We also show the compatibility withcrystalline Dieudonné theory and associated Galoisrepresentations. Our approach differs from Lau'sgeneralization of display theory, who independentlyobtained our result using display theory.

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