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Higher-level canonical subgroups for p-divisible groups

Part of: Algebraic groups Arithmetic algebraic geometry

Published online by Cambridge University Press:  13 December 2011

Joseph Rabinoff
Joseph Rabinoff
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA ([email protected])
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Abstract

Let R be a complete rank-1 valuation ring of mixed characteristic (0, p), and let K be its field of fractions. A g-dimensional truncated Barsotti–Tate group G of level n over R is said to have a level-n canonical subgroup if there is a K-subgroup of G ⊗RK with geometric structure (Z/pnZ)g consisting of points ‘closest to zero’. We give a non-trivial condition on the Hasse invariant of G that guarantees the existence of the canonical subgroup, analogous to a result of Katz and Lubin for elliptic curves. The bound is independent of the height and dimension of G.

Keywords

abelian varietiesp-divisible groupscanonical subgroupsautomorphic formstropical geometry

MSC classification

Secondary: 11G10: Abelian varieties of dimension $> 1$ 14L05: Formal groups, $p$-divisible groups
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 2 , April 2012 , pp. 363 - 419
Copyright
Copyright © Cambridge University Press 2012

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