HR-length of a free group via polynomial functors

Abstract

We prove that for a subring $R\subseteq \mathbb{Q}$ and a free group $F$ of rank at least $2$ the length of the Bousfield's $HR$-localization tower for $F$ is at least $\omega +\omega$. The key ingredient of the proof is the theory of polynomial functors over $\mathbb{Q}.$