{"paper":{"title":"Zero cycles on Severi--Brauer flag varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amit Hogadi, Divyasree C-Ramachandran","submitted_at":"2026-05-19T16:11:57Z","abstract_excerpt":"Let \\(A\\) be a central simple algebra over a field \\(F\\) with index \\(n\\) and let \\(\\mathrm{SB}_r(A)\\) denote the \\(r\\)-th generalized Severi--Brauer variety associated with \\(A\\). We prove that the Chow group of zero cycles of degree zero \\(\\mathrm{A_0}(\\mathrm{SB}_r(A))\\) is \\((d, n/d)\\)-torsion where \\(d = (r,n)\\). Our approach reduces the general case to division algebras of prime power index and yields several new instances in which \\(\\mathrm{A_0}\\) is trivial, together with sharper torsion bounds in general.\\\\ We also show that if \\(F\\) is a local or global field, then \\(\\mathrm{A_0}(\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20053","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/2605.20053/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"}