Higher-level canonical subgroups for p-divisible groups

Details Higher-level canonical subgroups for p-divisible groups Higher-level canonical subgroups for p-divisible groups

2009-10-17

arxiv.org/abs/0910.3323v2

Mathematics

Number Theory

43 pages, 5 figures, part of the author's Ph.D. thesis. Final version, to appear in the Journal of the Institute of Mathematic

Scientific paper

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\tensor_R K with geometric structure (\Z/p^n\Z)^g consisting of points "closest to zero". We give a nontrivial 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.

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