Let k be a perfect field of characteristic p > 2 and K an extension of F = FracW(k) contained in some F(μpr ). Using crystalline Dieudonné; theory, we provide a classification of p-divisible groups over R = OK[[t1,. ., td]] in terms of finite height (Ρ, τ)-modules over S := W(k)[[u, t1,. ., td]]. When d = 0, such a classification is a consequence of (a special case of) the theory of Kisin-Ren; in this setting, our construction gives an independent proof of this result, and moreover allows us to recover the Dieudonné; crystal of a p-divisible group from the Wach module associated to its Tate module by Berger-Breuil or by Kisin-Ren.
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