Geodesic
Purity results for $p$-divisible groups and Abelian schemes over regular bases of mixed characteristic
Documenta mathematica, Tome 15 (2010), pp. 571-599
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Let p be a prime. Let (R,m) be a regular local ring of mixed characteristic (0,p) and absolute index of ramification e. We provide general criteria of when each abelian scheme over SpecR∖m extends to an abelian scheme over SpecR. We show that such extensions always exist if e≤p−1, exist in most cases if p≤e≤2p−3, and do not exist in general if e≥2p−2. The case e≤p−1 implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring O of mixed characteristic (0,p) and index of ramification at most p−1. This leads to large classes of examples of Néron models over O. If p>2 and index p−1, the examples are new.
DOI : 10.4171/dm/307
Classification : 11G10, 11G18, 14F30, 14G35, 14G40, 14J20, 14K10, 14K15, 14L05, 14L15
Mots-clés : rings, Shimura varieties, group schemes, p-divisible groups, breuil windows and modules, abelian schemes, and Néron models 
@article{10_4171_dm_307,
     author = {Adrian Vasiu and Thomas Zink},
     title = {Purity results for $p$-divisible groups and {Abelian} schemes over regular bases of mixed characteristic},
     journal = {Documenta mathematica},
     pages = {571--599},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/307},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/307/}
}
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Adrian Vasiu; Thomas Zink. Purity results for $p$-divisible groups and Abelian schemes over regular bases of mixed characteristic. Documenta mathematica, Tome 15 (2010), pp. 571-599. doi: 10.4171/dm/307

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