Canonical Witt formal scheme extensions and p -torsion groups

We study the n th arithmetic jet space of the p -torsion subgroup attached to a smooth commutative formal group scheme. We show that the n th jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length n and the p -torsion subgroup we started with. This result generalizes a result of Buium on roots of unity.