Canonical subgroups via Breuil-Kisin modules for p=2

TL;DR

This paper establishes the existence of higher canonical subgroups for truncated Barsotti-Tate groups over p-adic fields, including the case p=2, under certain Hodge height conditions.

Contribution

It extends the theory of canonical subgroups to the case p=2, providing new existence results for higher canonical subgroups in this setting.

Findings

Existence of higher canonical subgroups under specified Hodge height conditions

Includes the case p=2, previously less understood

Provides properties of these subgroups in the context of p-adic Hodge theory

Abstract

Let p be a rational prime and K/Q_p 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 O_K with 0<d<h. In this paper, we prove the existence of higher canonical subgroups with expected properties for G if the Hodge height of G is less than 1/(p^{n-2}(p+1)), including the case of p=2.