Bijakowski, Stephane Partial Hasse invariants, partial degrees, and the canonical subgroup. (English) Zbl 1446.11105 Can. J. Math. 70, No. 4, 742-772 (2018). Summary: If the Hasse invariant of a \(p\)-divisible group is small enough, then one can construct a canonical subgroup inside its \(p\)-torsion. We prove that, assuming the existence of a subgroup of adequate height in the \(p\)-torsion with high degree, the expected properties of the canonical subgroup can be easily proved, especially the relation between its degree and the Hasse invariant. When one considers a \(p\)-divisible group with an action of the ring of integers of a (possibly ramified) finite extension of \(\mathbb{Q}_p\), then much more can be said. We define partial Hasse invariants (they are natural in the unramified case, and generalize a construction of D. A. Reduzzi and L. Xiao [Ann. Sci. Éc. Norm. Supér. (4) 50, No. 3, 579–607 (2017; Zbl 1430.11061)] in the general case), as well as partial degrees. After studying these functions, we compute the partial degrees of the canonical subgroup. Cited in 3 Documents MSC: 11F85 \(p\)-adic theory, local fields 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11S15 Ramification and extension theory 14L05 Formal groups, \(p\)-divisible groups Keywords:canonical subgroup; Hasse invariant; \(p\)-divisible group Citations:Zbl 1430.11061 PDF BibTeX XML Cite \textit{S. Bijakowski}, Can. J. Math. 70, No. 4, 742--772 (2018; Zbl 1446.11105) Full Text: DOI arXiv OpenURL