Canonical subgroups of Barsotti-Tate groups

• 成果类型: Article
• 署名作者: Tian, Yichao
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 955-988
• 关键词: abelian-varieties

摘要

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.