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Canonical subgroups via Breuil–Kisin modules

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Abstract

Let \(p>2\) be a rational prime and \(K/ \mathbb Q _p\) be an extension of complete discrete valuation fields. Let \(\mathcal G \) be a truncated Barsotti–Tate group of level \(n\), height \(h\) and dimension \(d\) over \(\mathcal{O }_K\) with \(0<d<h\). In this paper, we show that if the Hodge height of \(\mathcal G \) is less than \(1/(p^{n-2}(p+1))\), then there exists a finite flat closed subgroup scheme of \(\mathcal G \) of order \(p^{nd}\) over \(\mathcal{O }_K\) with standard properties as the canonical subgroup.

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Acknowledgments

The author would like to thank the anonymous referee for many helpful comments and suggestions, which improved the paper considerably. The author was supported by Grant-in-Aid for Young Scientists B-21740023.

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  1. Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Shin Hattori

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  1. Shin Hattori
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Correspondence to Shin Hattori.

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Hattori, S. Canonical subgroups via Breuil–Kisin modules. Math. Z. 274, 933–953 (2013). https://doi.org/10.1007/s00209-012-1102-0

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