Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension

Details Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension

2008-08-20

arxiv.org/abs/0808.2792v3

Mathematics

Number Theory

20 pages. Final version to appear in Advanced Studies in Pure Mathematics, Proceeding of Algebraic and Arithmetic Structures o

Scientific paper

Let $k$ be a perfect field of characteristic $p \geq 3$. We classify $p$-divisible groups over regular local rings of the form $W(k)[[t_1,...,t_r,u]]/(u^e+pb_{e-1}u^{e-1}+...+pb_1u+pb_0)$, where $b_0,...,b_{e-1}\in W(k)[[t_1,...,t_r]]$ and $b_0$ is an invertible element. This classification was in the case $r = 0$ conjectured by Breuil and proved by Kisin.

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