On the Drinfeld moduli problem of $p$-divisible groups

Drinfeld proved that the p-adic upper half space $\Omega^d_F$ for a $p$-adic local field $F$ is the general fiber of a formal scheme which is the moduli space of special formal $O_D$-modules, where $D$ is a central division algebra with invariant $1/d$ over $F$.We give examples of other moduli problems of $p$-divisible formal groups which have general fiber $\Omega^d_F$. We show that, when $F / \mathbb{Q}_p$ is unramified, our moduli spaces actually agree with Drinfeld’s space. Using our results in the ramified case, P. Scholze has proved this in general. We also consider a variant for the Lubin–Tate moduli problem.

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Published 16 May 2017