On the Drinfeld moduli problem of p-divisible groups

TL;DR

This paper explores moduli spaces of formal p-divisible groups with additional structures, showing they are represented by p-adic formal schemes related to Drinfeld's p-adic halfspace, extending known results and establishing analogues for Lubin-Tate spaces.

Contribution

It constructs new moduli spaces of formal p-divisible groups with structures linked to Drinfeld and Lubin-Tate theories, expanding the understanding of their geometric and representational properties.

Findings

New moduli spaces are represented by p-adic formal schemes.

Generic fibers of these schemes are isomorphic to Drinfeld's p-adic halfspace.

Analogues are established for Lubin-Tate moduli spaces.

Abstract

Let $O_D$ be the ring of integers in a division algebra of invariant $1/n$ over a p-adic local field. Drinfeld proved that the moduli problem of special formal $O_D$-modules is representable by Deligne's formal scheme version of the Drinfeld p-adic halfspace. In this paper we exhibit other moduli spaces of formal $p$-divisible groups which are represented by $p$-adic formal schemes whose generic fibers are isomorphic to the Drinfeld p-adic halfspace. We also prove an analogue concerning the Lubin-Tate moduli space.