An inverse theorem for the uniformity seminorms associated with the action of $F^{\omega }$

Vitaly Bergelson, Terence Tao, Tamar Ziegler

Let $\F$ a finite field. We show that the universal characteristic factor for the Gowers-Host-Kra uniformity seminorm $U^k(\X)$ for an ergodic action $(T_g)_{g \in \F^ω}$ of the in…