The cohomology of motivic $A(2)$

摘要

Working over an algebraically closed field of characteristic zero, we compute the cohomology of the subalgebra $A(2)$ of the motivic Steenrod algebra that is generated by $Sq^1$, $Sq^2$, and $Sq^4$. The method of calculation is a motivic version of the May spectral sequence. Speculatively assuming that there is a “motivic modular forms” spectrum with certain properties, we use an Adams-Novikov spectral sequence to compute the homotopy of such a spectrum at the prime 2.