Canonical subgroups via Breuil-Kisin modules

Shin Hattori

doi:10.1007/s00209-012-1102-0

Canonical subgroups via Breuil-Kisin modules

Shin Hattori

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	933-953
Number of pages	21
Journal	Mathematische Zeitschrift
Volume	274
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-012-1102-0
Publication status	Published - Aug 2013

All Science Journal Classification (ASJC) codes

Mathematics(all)

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AB - Let p > 2 be a rational prime and K/ℚp be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over OK with 0 < d < h. In this paper, we show that if the Hodge height of G is less than 1/(pn-2(p + 1)), then there exists a finite flat closed subgroup scheme of G of order pnd over OK with standard properties as the canonical subgroup.

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