# Enchiridion: Vol. 3 (2017): Don Larson

Author
Don Larson (Catholic University of America)

Source Paper
The Adams-Novikov $E_2$-term for Behrens’ spectrum $Q(2)$ at the prime $3$
(arxiv:1407.3423)

Source Paper Abstract
We compute the Adams-Novikov $E_2$-term of a spectrum $Q(2)$ constructed by Behrens. The homotopy groups of $Q(2)$ are closely tied to the $3$-primary stable homotopy groups of spheres; in particular, they are conjectured to detect the homotopy beta family of Greek letter elements at the prime $3$. Our computation leverages techniques used by Behrens to compute the rational homotopy of $Q(2)$, and leads to a conjecture that the Adams-Novikov $E_2$-term for $Q(2)$ detects the algebraic beta family in the $BP$-based Adams-Novikov $E_2$-term for the $3$-local sphere.