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

TL;DR

This paper proves that every ergodic measure-preserving system of a certain algebraic structure is a factor of a more specific Abramov system, advancing the understanding of nilspace-theoretic approaches in ergodic theory.

Contribution

It establishes that all ergodic $F_p^$-systems of order $k$ are factors of Abramov systems of the same order, answering a significant open question.

Findings

Every ergodic $F_p^$-system of order $k$ is a factor of an Abramov system of order $k

Advances the nilspace-theoretic framework in ergodic theory

Addresses a question posed by Jamneshan, Shalom, and Tao

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.