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arXiv · 2509.11266

The cohomology of $\mathbb{R}$-motivic $\mathcal{A}(2)$

Konstantin Emming
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Abstract

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

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BibTeXRIS

Konstantin Emming. 2026-06-19. The cohomology of $\mathbb{R}$-motivic $\mathcal{A}(2)$. https://arxiv.org/abs/2509.11266

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