On the Whitehead theorem for nilpotent motivic spaces

Abstract

We improve some foundational connectivity results and the relative Hurewicz theorem in motivic homotopy theory, study functorial central series in motivic local group theory, establish the existence of functorial Moore--Postnikov factorizations for nilpotent morphisms of motivic spaces under a mild technical hypothesis and establish an analog of the Whitehead theorem for nilpotent motivic spaces. As an application, we deduce a surprising unstable motivic periodicity result.