Exterior powers of \(\pi\)-divisible modules over fields (Q2017181)

In many categories the existence of a natural tensor product, or exterior powers, is an innocent matter and would usually not deserve much attention. It is, however, an important question, for we would like to factor, say, an alternating pairing of objects over the second exterior power. For example, for Galois representations this should be innocent and a pairing on abelian varieties would induce such a pairing. However, as one moves to more geometric ``sources'' of Galois representations, the existence question becomes less and less clear. E.g., on the level of group schemes, it already requires a proof that such an exterior power is still representable as a group scheme itself. In the present paper, the author considers this question in the category of \(\pi\)-divisible modules (e.g., \(p\)-divisible modules à la Barsotti-Tate). Here, the existence of exterior powers is a rather delicate matter. They may, or may not exist, and the paper (as well as its sequel) give a clear and careful analysis of this problem, as well as a fundamental existence result.