{"paper":{"title":"The cohomology of $\\mathbb{R}$-motivic $\\mathcal{A}(2)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Konstantin Emming","submitted_at":"2025-09-14T13:41:42Z","abstract_excerpt":"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 $\\rho$-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 homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11266","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.11266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}