{"paper":{"title":"On the Chow and cohomology rings of moduli spaces of stable curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hannah Larson, Samir Canning","submitted_at":"2022-08-03T21:47:10Z","abstract_excerpt":"In this paper, we ask: for which $(g, n)$ is the rational Chow or cohomology ring of $\\overline{\\mathcal{M}}_{g,n}$ generated by tautological classes? This question has been fully answered in genus $0$ by Keel (the Chow and cohomology rings are tautological for all $n$) and genus $1$ by Belorousski (the rings are tautological if and only if $n \\leq 10$). For $g \\geq 2$, work of van Zelm shows the Chow and cohomology rings are not tautological once $2g + n \\geq 24$, leaving finitely many open cases. Here, we prove that the Chow and cohomology rings of $\\overline{\\mathcal{M}}_{g,n}$ are isomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.02357","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/2208.02357/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"}