Higher-level canonical subgroups for p-divisible groups

2009/10/17 by Joseph Rabinoff, Rabinoff, Joseph · 1 citation
Mathematics · #11G10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0910.3323

openalex publication_date 2009/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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\tensor_R K with geometric structure (\Z/pⁿ\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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