In Tate's famous paper about $p$-divisible groups, for any prime $p$ he asked whether there exist nontrivial $p$-divisible groups over $\mathbb Z$, i.e. $p$-divisible groups which are not a product of powers of $\mu_{p^\infty}$ and $\mathbb Q_p/ \mathbb Z_p $.

From works of V. A. Abrashkin, we know there exist nontrivial $p$-divisible groups for $p=2$ and some irregular primes. What about the general case? Do we know a lot of primes $p$ such that every $p$-divisible group over $\mathbb Z$ is trivial?