On measure-preserving $\mathbb{F}_p^\omega$-systems of order $k$

Abstract

Building on previous work in the nilspace-theoretic approach to the study of Host-Kra factors of measure-preserving systems, we prove that every ergodic $\mathbb{F}_p^\omega$-system of order $k$ is a factor of an Abramov $\mathbb{F}_p^\omega$-system of order $k$. This answers a question of Jamneshan, Shalom and Tao.