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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.20053","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-19T16:11:57Z","cross_cats_sorted":[],"title_canon_sha256":"3340c4fb9df723d7da4caa3e5762a1642ed3489ac0f3974e0cdeeec4e913727c","abstract_canon_sha256":"f1034614e5f05b31f99de04bb8fe658eec88dd940c707ab386ff75cef3ae97bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:06:00.291542Z","signature_b64":"eTw0fN/kDaBHMvXmhEcVnVsHCVCWoFb39bgemH4S4/Z3q47NjI1iJrdThG4frSOUI/VXwqSzbHPltLzJyYySAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abf800c8812843f2738534d4029b5ccf35decf1ab1367963b7ba2fac65cc04c6","last_reissued_at":"2026-05-20T02:06:00.291035Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:06:00.291035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.20053","created_at":"2026-05-20T02:06:00.291127+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20053v1","created_at":"2026-05-20T02:06:00.291127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20053","created_at":"2026-05-20T02:06:00.291127+00:00"},{"alias_kind":"pith_short_12","alias_value":"VP4ABSEBFBB7","created_at":"2026-05-20T02:06:00.291127+00:00"},{"alias_kind":"pith_short_16","alias_value":"VP4ABSEBFBB7E44F","created_at":"2026-05-20T02:06:00.291127+00:00"},{"alias_kind":"pith_short_8","alias_value":"VP4ABSEB","created_at":"2026-05-20T02:06:00.291127+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4","json":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4.json","graph_json":"https://pith.science/api/pith-number/VP4ABSEBFBB7E44FGTKAFG24Z4/graph.json","events_json":"https://pith.science/api/pith-number/VP4ABSEBFBB7E44FGTKAFG24Z4/events.json","paper":"https://pith.science/paper/VP4ABSEB"},"agent_actions":{"view_html":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4","download_json":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4.json","view_paper":"https://pith.science/paper/VP4ABSEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20053&json=true","fetch_graph":"https://pith.science/api/pith-number/VP4ABSEBFBB7E44FGTKAFG24Z4/graph.json","fetch_events":"https://pith.science/api/pith-number/VP4ABSEBFBB7E44FGTKAFG24Z4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4/action/storage_attestation","attest_author":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4/action/author_attestation","sign_citation":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4/action/citation_signature","submit_replication":"https://pith.science/pith/VP4ABSEBFBB7E44FGTKAFG24Z4/action/replication_record"}},"created_at":"2026-05-20T02:06:00.291127+00:00","updated_at":"2026-05-20T02:06:00.291127+00:00"}