Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic

Vasiu A, Zink T (2010)
Documenta Mathematica 15: 571-599.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Vasiu, Adrian; Zink, ThomasUniBi
Abstract / Bemerkung
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 Spec R \ {m} extends to an abelian scheme over Spec R. We show that such extensions always exist if e <= p-1, exist in most cases if p <= e <= 2 p-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 Neron models over O. If p > 2 and index p - 1, the examples are new.
Stichworte
Breuil windows and modules; rings; group schemes; Neron models; abelian schemes; Shimura varieties; p-divisible groups
Erscheinungsjahr
2010
Zeitschriftentitel
Documenta Mathematica
Band
15
Seite(n)
571-599
ISSN
1431-0643
Page URI
https://pub.uni-bielefeld.de/record/1793896

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Vasiu A, Zink T. Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic. Documenta Mathematica. 2010;15:571-599.
Vasiu, A., & Zink, T. (2010). Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic. Documenta Mathematica, 15, 571-599.
Vasiu, A., and Zink, T. (2010). Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic. Documenta Mathematica 15, 571-599.
Vasiu, A., & Zink, T., 2010. Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic. Documenta Mathematica, 15, p 571-599.
A. Vasiu and T. Zink, “Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic”, Documenta Mathematica, vol. 15, 2010, pp. 571-599.
Vasiu, A., Zink, T.: Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic. Documenta Mathematica. 15, 571-599 (2010).
Vasiu, Adrian, and Zink, Thomas. “Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic”. Documenta Mathematica 15 (2010): 571-599.

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