2025/09/14 by Konstantin Emming, Emming, Konstantin
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2509.11266
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.