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Canonical subgroups of Barsotti-Tate groups

Yichao Tian
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Abstract

Let $S$ be the spectrum of a complete discrete valuation ring with fraction field of characteristic 0 and perfect residue field of characteristic $p\geq 3$. Let $G$ be a truncated Barsotti-Tate group of level 1 over $S$. If ``$G$ is not too supersingular'', a condition that will be explicitly expressed in terms of the valuation of a certain determinant, we prove that we can canonically lift the kernel of the Frobenius endomorphism of its special fibre to a subgroup scheme of $G$, finite and flat over $S$. We call it the canonical subgroup of $G$.

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Yichao Tian. 2008-08-19. Canonical subgroups of Barsotti-Tate groups. https://arxiv.org/abs/math/0606059

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