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May 18, 2013 at 6:11 comment added TOM I haved see Illusie's paper, it is true even in some affine case ($X$ is affine ), but I think it may has obstruction in case of smooth projective curve.
May 17, 2013 at 18:08 history edited user9072
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May 17, 2013 at 13:22 comment added user28172 Yes; see Illusie's paper that surveys Grothendieck's work on the deformation theory of p-divisible groups. Early in there he gives Dieudonne-module arguments of Gabber and Ekedahl to handle the extension problem over any perfect field.
May 17, 2013 at 12:21 history asked TOM CC BY-SA 3.0