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VOL. 58 | 2010 Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension

Abstract

Let $k$ be a perfect field of characteristic $p \geq 3$. We classify $p$-divisible groups over regular local rings of the form $$ W(k) [[t_1, \dots, t_r, u]]/(u^e + pb_{e-1} u^{e-1} + \dots + pb_1 u + pb_0), $$ where $b_0, \dots, b_{e-1} \in W(k) [[t, \dots, t_r]]$ and $b_0$ is an invertible element. This classification was in the case $r = 0$ conjectured by Breuil and proved by Kisin.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1210.14049
MathSciNet: MR2676165

Digital Object Identifier: 10.2969/aspm/05810461

Subjects:
Primary: 11G10, 11G18, 14F30, 14G35, 14K10, 14L05

Rights: Copyright © 2010 Mathematical Society of Japan

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