The Drinfeld moduli conjecture for special p-divisible groups

Let FF be the relevant base field, let ODO_D be the specified maximal order, and fix an rr-special pp-divisible group (X,ιX)({\mathbb {X}},\iota_{{\mathbb {X}}}) over an algebraic closure kˉ\bar k of the residue field of OE˘O_{\breve E}. For SNilpOE˘S\in {\rm Nilp}_{O_{\breve E}}, let Mr(S)\mathcal{M}_r(S) be the set of isomorphism classes of triples (X,ι,ϱ)(X,\iota,\varrho), where (X,ι)(X,\iota) is an rr-special ODO_D-module over SS and ϱ\varrho is an ODO_D-linear quasi-isogeny of height zero from X×SSˉX\times_S\bar S to X×SpeckˉSˉ\mathbb{X}\times_{\operatorname{Spec}\bar k}\bar S. Drinfeld moduli conjecture. The functor Mr\mathcal{M}_r is represented by

Ω^Fn^OFOE˘.\hat{\Omega}^n_F\hat{\otimes}_{O_F}O_{\breve E}.

This identifies the moduli problem for rr-special pp-divisible groups with the formal Drinfeld space after base change to OE˘O_{\breve E}; the source presents this as its main conjecture, and no resolution is supplied in the provided text.

Sources & referencesView supporting material

Primary source

M. Rapoport and Th. Zink, “On the Drinfeld moduli problem of p-divisible groups”, arXiv:1408.4071 (2017).

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