Canonical subgroups via Breuil–Kisin modules for [formula omitted

Abstract

Let p be a rational prime and K/Qp be an extension of complete discrete valuation fields. Let G be a truncated Barsotti–Tate group of level n, height h and dimension d over OK with 0<d<h. In this paper, we prove the existence of higher canonical subgroups for G with standard properties if the Hodge height of G is less than 1/(pn−2(p+1)), including the case of p=2.