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Crystalline Dieudonné theory over excellent schemes. (English) Zbl 0963.14008
Let \(\mathbb{D}\) stand for the crystalline Dieudonné module functor on \(p\)-divisible groups over a base \(S\) of characteristic \(p\). The main results are: the full-faithfulness of \(\mathbb{D}\) over excellent local complete intersection schemes, and the full-faithfulness of \(\mathbb{D}\) up to isogeny when \(S\) is local excellent.


The authors make use of D. Popescu’s strong Néron desingularization [D. Popescu, Nagoya Math. J. 100, 97-126 (1985; Zbl 0561.14008)] and the extension theorem for homomorphisms of \(p\)-divisible groups of A. J. de Jong [Invent. Math. 134, No. 2, 301-333 (1998; Zbl 0929.14029); Erratum: ibid. 138, No. 1, 225 (1999)]. They also prove results concerning the faithfulness for the Dieudonné functor on finite locally free group schemes (there are examples where it is not faithful).

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
14L05 Formal groups, \(p\)-divisible groups
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