What type of study is this?

This is a Cohort Study study (also classified as: Quantitative Study).

October 13, 2025Open Access

The cohomology of R-motivic A (2)

Key Points

The cohomology of the quotient algebra $mathcal{A}(2)$ is computed using a Bockstein spectral sequence.
Input from $mathbb{C}$-motivic $mathcal{A}(2)$ guides the spectral sequence approach for the computation.
Cohomology results could influence the Adams spectral sequence of an R-motivic modular forms spectrum.
Findings may ultimately provide insights into the homotopy groups of the R-motivic sphere spectrum.

Abstract

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.

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Cite This Study

Konstantin Emming (Sun,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0941f https://doi.org/https://doi.org/10.48550/arxiv.2509.11266

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