TY - JOUR

T1 - Dieudonné; crystals and Wach modules for p-divisible groups

AU - Cais, Bryden

AU - Lau, Eike

N1 - Publisher Copyright:
© 2017 London Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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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U2 - 10.1112/plms.12021

DO - 10.1112/plms.12021

M3 - Article

AN - SCOPUS:85025131021

SN - 0024-6115

VL - 114

SP - 733

EP - 763

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 4

ER -