A $v_1$-banded vanishing line for the mod 2 Moore spectrum

Abstract

The mod 2 Moore spectrum $C(2)$ is the cofiber of the self-map $2: \mathbb{S} \to \mathbb{S}$. Building on work of Burklund, Hahn, and Senger, we prove that above a line of slope $\frac{1}{5}$, the Adams spectral sequence for $C(2)$ collapses at its $E_5$-page and characterize the surviving classes. This completes the proof of a result of Mahowald, announced in 1970, but never proven.