# Canonical subgroups of Barsotti-Tate groups | Annals of Mathematics

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≥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, then we prove that we can canonically lift the kernel of the Frobenius endomorphism of its special fiber to a subgroup scheme of G, finite and flat over S. We call it the canonical subgroup of G.

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### 数学年刊（Annals of Mathematics）

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