de Jong, Aise Johan; Messing, William Crystalline Dieudonné theory over excellent schemes. (English) Zbl 0963.14008 Bull. Soc. Math. Fr. 127, No. 2, 333-348 (1999). 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). Reviewer: Eyal Z.Goren (Montreal) Cited in 5 Documents MSC: 14F30 \(p\)-adic cohomology, crystalline cohomology 14L05 Formal groups, \(p\)-divisible groups Keywords:crystalline Dieudonné module functor; characteristic \(p\); \(p\)-divisible groups; Barsotti-Tate group; crystalline cohomology Citations:Zbl 0575.14010; Zbl 0561.14008; Zbl 0929.14029 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML Link References: [1] BERTHELOT (P.) . - Cohomologie rigide et cohomologie rigide à support propre , version provisoire du 9-08- 1991 . · Zbl 0515.14015 [2] BERTHELOT (P.) , BREEN (L.) , MESSING (W.) . - Théorie de Dieudonné cristalline , II, Lecture Notes in Mathematics 930, Springer Verlag, 1982 . MR 85k:14023 | Zbl 0516.14015 · Zbl 0516.14015 [3] BERTHELOT (P.) , MESSING (W.) . - Théorie de Dieudonné cristalline , III, in The Grothendieck Festschrift I, Progress in Math. 86, Birkhäuser, 1990 , p. 171-247. MR 92h:14012 | Zbl 0753.14041 · Zbl 0753.14041 [4] DE JONG (A.J.) . - Crystalline Dieudonné module theory via formal and rigid geometry , Publications Math., t. 82, 1995 , p. 5-96. Numdam | MR 97f:14047 | Zbl 0864.14009 · Zbl 0864.14009 · doi:10.1007/BF02698637 [5] DE JONG (A.J.) . - Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic , Invent. Math., t. 134, 1998 . MR 2000f:14070a | Zbl 0929.14029 · Zbl 0929.14029 · doi:10.1007/s002220050266 [6] KIMURA (T.) , NIITSUMA (N.) . - Regular local rings of characteristic p and p-basis , J. Math. Soc. Japan, t. 32, 1980 , p. 363-371. Article | MR 81j:13022 | Zbl 0451.13010 · Zbl 0451.13010 · doi:10.2969/jmsj/03220363 [7] OORT (F.) . - Commutative group schemes , Lecture Notes in Mathematics 15, Springer, 1966 . MR 35 #4229 | Zbl 0216.05603 · Zbl 0216.05603 · doi:10.1007/BFb0097479 [8] POPESCU (D.) . - General Néron desingularization , Nagoya Math. J., t. 100, 1985 , p. 97-126. Article | MR 87f:13019 | Zbl 0561.14008 · Zbl 0561.14008 [9] SWAN (R.G.) . - Néron-Popescu desingularization , Lecture Notes of the University of Chicago, 1995 ; to appear in Proceedings of the International Conference on Algebra and Geometry, Taipei (Taiwan, 1995 ), p. 1-44. [10] DEMAZURE (M.) , GROTHENDIECK (A.) . - SGA3, Schémas en groupes , I, Lecture Notes in Math. 151, Springer Verlag, 1970 . MR 43 #223a | Zbl 0207.51401 · Zbl 0207.51401 · doi:10.1007/BFb0058993 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.