The cohomology of R-motivic A (2)

We compute the cohomology of the quotient algebra A (2) of the R-motivic dual Steenrod algebra. We do so by running a ρ-Bockstein spectral sequence whose input is the cohomology of C-motivic A (2). The purpose of our computation is that the cohomology of A (2) is the input to an Adams spectral sequence of a hypothetical R-motivic modular forms spectrum. This Adams spectral sequence computes the homotopy groups of such an R-motivic modular forms spectrum, which in turn can be used to make inferences about the homotopy groups of the R-motivic sphere spectrum and eventually about the classical stable stems.