{"paper":{"title":"Homogeneous spaces in tensor categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Sherman, Kevin Coulembier","submitted_at":"2025-05-07T22:54:46Z","abstract_excerpt":"Let $\\mathscr{C}$ be a symmetric tensor category of moderate growth, and let $\\mathcal{H}\\leq\\mathcal{G}$ be algebraic groups in $\\mathscr{C}$. We prove that the homogeneous space $\\mathcal{G}/\\mathcal{H}$ exists as a scheme and is of finite type when $\\mathscr{C}$ is geometrically reductive and maximally nilpotent, conditions that are conjecturally equivalent to incompressibility. A key tool is the introduction of a Frobenius kernel of an group scheme. We further show that while $\\mathcal{G}_0/\\mathcal{H}_0$ and $(\\mathcal{G}/\\mathcal{H})_0$ need not be the same, they are close enough, so tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04848","kind":"arxiv","version":3},"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/2505.04848/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"}