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Level \(m\) stratifications of versal deformations of \(p\)-divisible groups. (English) Zbl 1152.14022
For a \(p\)-divisible group \(G\) over a perfect field \(k\) (of characteristic \(p\)) there exists a versal deformation. The paper under review describes a locally closed subscheme whose \(k\)-points are precisely the points where the universal deformation is isomorphic to the original group. The proof uses Traverso’s theorem that a \(p\)-divisible group is determined by its truncation of suitably high order \(n\), and the Dieudonné-crystal of the universal group over the Witt vectors of length \(n\) over the versal deformation. At the end the results are extended to \(p\)-divisible groups of Hodge type, which amounts to replacing the general linear group \(\text{GL}(m)\) by certain reductive subgroups.

MSC:
14G35 Modular and Shimura varieties
14L05 Formal groups, \(p\)-divisible groups
11G18 Arithmetic aspects of modular and Shimura varieties
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