Exterior Powers of Lubin-Tate Groups

Let O be the ring of integers of a non-Archimedean local field of characteristic zero and pi a fixed uniformizer of O. We prove that the exterior powers of a pi-divisible module of dimension at most 1 over a locally Noetherian scheme exist and commute with arbitrary base change. We calculate the height and dimension of the exterior powers in terms of the height of the given pi-divisible module. In the case of p-divisible groups, the existence of the exterior powers are proved without any condition on the basis.