{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:XKAPLFC77PR6LEEGDYAWUVMJCH","short_pith_number":"pith:XKAPLFC7","schema_version":"1.0","canonical_sha256":"ba80f5945ffbe3e590861e016a558911e807df6c58a260c20e48edc86aa649f1","source":{"kind":"arxiv","id":"0905.1538","version":1},"attestation_state":"computed","paper":{"title":"Approximating classifying spaces by smooth projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Torsten Ekedahl","submitted_at":"2009-05-11T04:27:22Z","abstract_excerpt":"We prove that for every reductive algebraic group $H$ with centre of positive dimension and every integer $K$ there is a smooth and projective variety $X$ and an algebraic $H$-torsor $P \\to X$ such that the classifying map $X \\to \\Bclass H$ induces an isomorphism in cohomology in degrees $\\le K$. This is then applied to show that if $G$ is a connected non-special group there is a $G$-torsor $P \\to X$ for which we do not have $[P]=[G][X]$ in the (completion of the) Grothendieck ring of varieties."},"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":"0905.1538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-11T04:27:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c03323b0e1f3d339ae4e6ba84d0eb66150eaeba3b65806fd2d80332a78b01dc6","abstract_canon_sha256":"97d22014590918948e7a931642bf7f1278bfea69fa9a5e240821a29d63d9f913"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:42:21.931180Z","signature_b64":"t+W9DcIkvbhagc6MaqSlZp4z28eq12DFZpxszjwCIF39haFLjebwRfLa0jkbnWLkHEbtd2CdjkAvlv3jswAJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba80f5945ffbe3e590861e016a558911e807df6c58a260c20e48edc86aa649f1","last_reissued_at":"2026-07-04T15:42:21.930808Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:42:21.930808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating classifying spaces by smooth projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Torsten Ekedahl","submitted_at":"2009-05-11T04:27:22Z","abstract_excerpt":"We prove that for every reductive algebraic group $H$ with centre of positive dimension and every integer $K$ there is a smooth and projective variety $X$ and an algebraic $H$-torsor $P \\to X$ such that the classifying map $X \\to \\Bclass H$ induces an isomorphism in cohomology in degrees $\\le K$. This is then applied to show that if $G$ is a connected non-special group there is a $G$-torsor $P \\to X$ for which we do not have $[P]=[G][X]$ in the (completion of the) Grothendieck ring of varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1538","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/0905.1538/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":"0905.1538","created_at":"2026-07-04T15:42:21.930867+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.1538v1","created_at":"2026-07-04T15:42:21.930867+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1538","created_at":"2026-07-04T15:42:21.930867+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKAPLFC77PR6","created_at":"2026-07-04T15:42:21.930867+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKAPLFC77PR6LEEG","created_at":"2026-07-04T15:42:21.930867+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKAPLFC7","created_at":"2026-07-04T15:42:21.930867+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/XKAPLFC77PR6LEEGDYAWUVMJCH","json":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH.json","graph_json":"https://pith.science/api/pith-number/XKAPLFC77PR6LEEGDYAWUVMJCH/graph.json","events_json":"https://pith.science/api/pith-number/XKAPLFC77PR6LEEGDYAWUVMJCH/events.json","paper":"https://pith.science/paper/XKAPLFC7"},"agent_actions":{"view_html":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH","download_json":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH.json","view_paper":"https://pith.science/paper/XKAPLFC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.1538&json=true","fetch_graph":"https://pith.science/api/pith-number/XKAPLFC77PR6LEEGDYAWUVMJCH/graph.json","fetch_events":"https://pith.science/api/pith-number/XKAPLFC77PR6LEEGDYAWUVMJCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH/action/storage_attestation","attest_author":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH/action/author_attestation","sign_citation":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH/action/citation_signature","submit_replication":"https://pith.science/pith/XKAPLFC77PR6LEEGDYAWUVMJCH/action/replication_record"}},"created_at":"2026-07-04T15:42:21.930867+00:00","updated_at":"2026-07-04T15:42:21.930867+00:00"}