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

TL;DR

This paper proves a long-standing conjecture about the collapse of the Adams spectral sequence for the mod 2 Moore spectrum above a specific line, completing a 50-year-old mathematical result.

Contribution

It establishes a $v_1$-banded vanishing line for the Adams spectral sequence of the mod 2 Moore spectrum, confirming a conjecture from 1970.

Findings

Spectral sequence collapses above a slope 1/5 line at the $E_5$-page.

Characterization of the classes that survive beyond the collapse.

Completes the proof of Mahowald's 1970 conjecture.

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.