The Drinfeld moduli conjecture for special p-divisible groups

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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 S∈NilpOE˘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×Spec⁡kˉSˉ\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.

References

Primary source

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

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