Towards the $p=3$ Kervaire Invariant Problem: The $E_2$-page for the homotopy fixed points spectral sequence computing ${\pi }_{\ast }({E_6}^{h{C}_9})$

Abstract

Hill, Hopkins, and Ravenel suggest that the last remaining Kervaire invariant problem, the case of $p=3$, can be solved by computing the homotopy fixed points spectral sequence for ${\pi }_{\ast }{E}_6^{h{C}_9}$. We prove a detection theorem for this case and use a conjectural form of the $C_9$-action on $E_6$ to compute the $E_2$ page of this spectral sequence away from homological degree zero.