Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic

Vasiu A, Zink T (2012)
Journal of Number Theory 132(9): 2003-2019.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Vasiu, Adrian; Zink, ThomasUniBi
Abstract / Bemerkung
Let p be a prime. Let V be a discrete valuation ring of mixed characteristic (0, p) and index of ramification e. Let f : G -> H be a homomorphism of finite flat commutative group schemes of p power order over V whose generic fiber is an isomorphism. We provide a new proof of a result of Bondarko and Liu that bounds the kernel and the cokernel of the special fiber of f in terms of e. For e < p - 1 this reproves a result of Raynaud. Our bounds are sharper that the ones of Liu, are almost as sharp as the ones of Bondarko, and involve a very simple and short method. As an application we obtain a new proof of an extension theorem for homomorphisms of truncated Barsotti-Tate groups which strengthens Tate's extension theorem for homomorphisms of p-divisible groups. (C) 2012 Elsevier Inc. All rights reserved.
Stichworte
Discrete valuation rings; Group schemes; Truncated Barsotti-Tate groups; p-divisible groups; Breuil modules
Erscheinungsjahr
2012
Zeitschriftentitel
Journal of Number Theory
Band
132
Ausgabe
9
Seite(n)
2003-2019
ISSN
0022-314X
Page URI
https://pub.uni-bielefeld.de/record/2523678

Zitieren

Vasiu A, Zink T. Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic. Journal of Number Theory. 2012;132(9):2003-2019.
Vasiu, A., & Zink, T. (2012). Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic. Journal of Number Theory, 132(9), 2003-2019. doi:10.1016/j.jnt.2012.03.010
Vasiu, A., and Zink, T. (2012). Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic. Journal of Number Theory 132, 2003-2019.
Vasiu, A., & Zink, T., 2012. Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic. Journal of Number Theory, 132(9), p 2003-2019.
A. Vasiu and T. Zink, “Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic”, Journal of Number Theory, vol. 132, 2012, pp. 2003-2019.
Vasiu, A., Zink, T.: Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic. Journal of Number Theory. 132, 2003-2019 (2012).
Vasiu, Adrian, and Zink, Thomas. “Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic”. Journal of Number Theory 132.9 (2012): 2003-2019.

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