{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CNFKNRWSVLLIFLQTEUOD6ILKVM","short_pith_number":"pith:CNFKNRWS","schema_version":"1.0","canonical_sha256":"134aa6c6d2aad682ae13251c3f216aab34a44478eefd00f596b357fea53f8f30","source":{"kind":"arxiv","id":"1009.2011","version":3},"attestation_state":"computed","paper":{"title":"On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kang Zuo, Mao Sheng, Stefan M\\\"uller-Stach, Xuanming Ye","submitted_at":"2010-09-10T13:34:01Z","abstract_excerpt":"Let $X$ be a Hilbert modular variety and $\\mathbb{V}$ a non-trivial local system over $X$ with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the cohomology group $H^k(X,\\mathbb{V})$ using the method of Higgs bundles. Among other results we prove the Eichler-Shimura isomorphism, give a dimension formula for the Hodge numbers and show that the mixed Hodge structure is split over $\\mathbb{R}$. These results are analogous to Matsushima-Shimura [Annals of Mathematics 78, 1963] in the cocompact case and complement the results in Freitag [Book: Hilbert modular form"},"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":"1009.2011","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-10T13:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"a759a47ff1e6c2b80f603afae4a0b1e10178b1ed62d0fa92718effa57f9782b9","abstract_canon_sha256":"075e0ce1dfbd28a5d2fb3cbb598d690ea6664fc1b6c076a1f3f8f792d934a299"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:54.499075Z","signature_b64":"O+X0uhhtCmcFU7yjtPIBzt5yxYUBrZHxs0H/TS/3mUCvRALPaxiGXVy/5+C4jJBK3gY9jVB0LbJyrjZ1QTGACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"134aa6c6d2aad682ae13251c3f216aab34a44478eefd00f596b357fea53f8f30","last_reissued_at":"2026-05-18T02:42:54.498616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:54.498616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kang Zuo, Mao Sheng, Stefan M\\\"uller-Stach, Xuanming Ye","submitted_at":"2010-09-10T13:34:01Z","abstract_excerpt":"Let $X$ be a Hilbert modular variety and $\\mathbb{V}$ a non-trivial local system over $X$ with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the cohomology group $H^k(X,\\mathbb{V})$ using the method of Higgs bundles. Among other results we prove the Eichler-Shimura isomorphism, give a dimension formula for the Hodge numbers and show that the mixed Hodge structure is split over $\\mathbb{R}$. These results are analogous to Matsushima-Shimura [Annals of Mathematics 78, 1963] in the cocompact case and complement the results in Freitag [Book: Hilbert modular form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2011","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":""},"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":"1009.2011","created_at":"2026-05-18T02:42:54.498698+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2011v3","created_at":"2026-05-18T02:42:54.498698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2011","created_at":"2026-05-18T02:42:54.498698+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNFKNRWSVLLI","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNFKNRWSVLLIFLQT","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNFKNRWS","created_at":"2026-05-18T12:26:06.534383+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/CNFKNRWSVLLIFLQTEUOD6ILKVM","json":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM.json","graph_json":"https://pith.science/api/pith-number/CNFKNRWSVLLIFLQTEUOD6ILKVM/graph.json","events_json":"https://pith.science/api/pith-number/CNFKNRWSVLLIFLQTEUOD6ILKVM/events.json","paper":"https://pith.science/paper/CNFKNRWS"},"agent_actions":{"view_html":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM","download_json":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM.json","view_paper":"https://pith.science/paper/CNFKNRWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2011&json=true","fetch_graph":"https://pith.science/api/pith-number/CNFKNRWSVLLIFLQTEUOD6ILKVM/graph.json","fetch_events":"https://pith.science/api/pith-number/CNFKNRWSVLLIFLQTEUOD6ILKVM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM/action/storage_attestation","attest_author":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM/action/author_attestation","sign_citation":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM/action/citation_signature","submit_replication":"https://pith.science/pith/CNFKNRWSVLLIFLQTEUOD6ILKVM/action/replication_record"}},"created_at":"2026-05-18T02:42:54.498698+00:00","updated_at":"2026-05-18T02:42:54.498698+00:00"}