$p$-divisible groups over $\mathbf Z$

In this paper it is shown that:
a) there do not exist 3-dimensional abelian varieties over $\mathbf Q$ having everywhere good reduction:
b) every 2-divisible group over $\mathbf Z$ of height $\leqslant6$ is isogenous to the trivial one;
c) for irregular primes $p$ there exist nontrivial $p$-divisible groups over $\mathbf Z$.
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