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Tian, Yichao

Canonical subgroups of Barsotti-Tate groups. (English) Zbl 1203.14026

Ann. Math. (2) 172, No. 2, 955-988 (2010).
The paper under review generalises a theorem of A. Abbes and A. Mokrane [Publ. Math. Inst. Hautes Etud. Sci. 99, 117–162 (2004; Zbl 1062.14057)]. Assume \(V\) is a discrete valuation-ring of mixed characteristic \(p\), with perfect residue field, and \(G\) a truncated Barsotti-Tate group of level one over \(V\). Modulo \(p\) kernel of Frobenius defines a finite flat closed subscheme. The problem is to find a finite flat lift to \(V\). This is known for ordinary \(G\)’s, and shown here if the determinant of the adjoint Frobenius (the Verschiebung) on the Lie-algebra of the dual group has sufficiently small valuation (this valuation is zero for ordinary \(G\)). The lift is characterised by either the ramification theory of Abbes-Saito or by a refinement of Cartier-duality. The proof uses heavily the filtration on mod \(p\) vanishing cycles defined by Bloch-Kato.
Reviewer: Gerd Faltings (Bonn)

Cited in 1 Review
Cited in 8 Documents

MSC:

14F30 \(p\)-adic cohomology, crystalline cohomology

Keywords:

canonical subgroup; ramification filtration

Citations:

Zbl 1062.14057
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Full Text: DOI arXiv

References:

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