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(1) In the definition of Dieudonné crystal [?, Definition 3.1], the condition on the filtration [?, Definition 3.1(3)] should be replaced by requiring Fil EX to be an admissible filtration, as introduced by Grothendieck [Gro74, Ch. V, §3]. We recall the definition below (cf. Definition 1), and verify that the Hodge filtration for any p-divisible group G over X is admissible (cf. Lemma 3), which makes D∗(G) a Dieudonné crystal according to the corrected definition. (2) The statement of [?, Proposition 3.8] holds for the corrected definition of Dieudonné crystal. In §2, we explain how to correct the proof of [?, Proposition 3.8].

Erratum to “The Relative Breuil-Kisin Classification of p -Divisible Groups and Finite Flat Group Schemes”