Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Breuil's classification of $p$-divisible groups over regular local rings
  of arbitrary dimension   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.

5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th