{"paper":{"title":"Noncommutative Cartier Formulae","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG","math.KT","math.SG"],"primary_cat":"math.AT","authors_text":"Semon Rezchikov","submitted_at":"2026-07-06T17:36:47Z","abstract_excerpt":"We prove, for every $\\mathbb{E}_1$ algebra $A$, a formula describing the interaction of the action of the cap product on topological Hochschild homology of $A$ with the cyclotomic structure map, as well as a variant of this result relative to a ring $R$. Specializing to $R = \\mathbb{F}_p$ gives a noncommutative analog of a formula of Cartier which describes the conjugation of interior product action on differential forms by the Cartier isomorphism, and which computes the $p$-curvature of the Getzler-Gauss-Manin connection in terms of an equivariant cap product. The motivation for this formula "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05360","kind":"arxiv","version":1},"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/2607.05360/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"}