On the Whitehead theorem for nilpotent motivic spaces

TL;DR

This paper advances foundational results in motivic homotopy theory, including a Whitehead theorem for nilpotent motivic spaces, and demonstrates a surprising unstable motivic periodicity, broadening understanding of motivic spaces.

Contribution

It establishes a Whitehead theorem for nilpotent motivic spaces and develops functorial Moore–Postnikov factorizations under mild conditions, enhancing the theoretical framework.

Findings

Proved a Whitehead theorem for nilpotent motivic spaces

Established functorial Moore–Postnikov factorizations

Discovered an unstable motivic periodicity phenomenon

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.