{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PFWFT7JWQHSSFKXXRZGXJANQII","short_pith_number":"pith:PFWFT7JW","schema_version":"1.0","canonical_sha256":"796c59fd3681e522aaf78e4d7481b04210e61d36b0e07c7de8c4df1b324eeea4","source":{"kind":"arxiv","id":"2506.06246","version":1},"attestation_state":"computed","paper":{"title":"On Hodge--Witt cohomology of Drinfeld's upper half space over a finite field","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Mattia Tiso","submitted_at":"2025-06-06T17:11:59Z","abstract_excerpt":"In this dissertation we study the Hodge-Witt cohomology of the $d$-dimensional Drinfeld's upper half space $\\mathcal{X} \\subset \\mathbb{P}_k^d$ over a finite field $k$. We consider the natural action of the $k$-rational points $G$ of the linear group $\\mathrm{GL}_{d+1}$ on $H^0(\\mathcal{X},\\mathrm{W}_n\\Omega_{\\mathbb{P}_k^d}^i)$, making them natural $\\mathrm{W}_n(k)[G]$-modules. To study these representations, we introduce a theory of differential operators over the Witt vectors for smooth $k$-schemes $X$, through a quasi-coherent sheaf of $\\mathrm{W}_n(k)$-algebras $\\mathcal{D}_{\\mathrm{W}_n("},"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":"2506.06246","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-06T17:11:59Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"5549e2f3c35abbc1533cc34744063d3be1a7d848304e9da2cac91c5829460388","abstract_canon_sha256":"65d78b8212f0779380b7697434a4c06d69466e70c66323dc488a7e46fd74a218"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:28.093194Z","signature_b64":"D1Gb6uTYYZz1q/yNdDyvHOmI/W+GpmLChhJCN6t2XXXUCcZNeuejA4KlCnsMBMnhEDbq7X591faQGRsiZL6iDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"796c59fd3681e522aaf78e4d7481b04210e61d36b0e07c7de8c4df1b324eeea4","last_reissued_at":"2026-07-05T11:17:28.092680Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:28.092680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hodge--Witt cohomology of Drinfeld's upper half space over a finite field","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Mattia Tiso","submitted_at":"2025-06-06T17:11:59Z","abstract_excerpt":"In this dissertation we study the Hodge-Witt cohomology of the $d$-dimensional Drinfeld's upper half space $\\mathcal{X} \\subset \\mathbb{P}_k^d$ over a finite field $k$. We consider the natural action of the $k$-rational points $G$ of the linear group $\\mathrm{GL}_{d+1}$ on $H^0(\\mathcal{X},\\mathrm{W}_n\\Omega_{\\mathbb{P}_k^d}^i)$, making them natural $\\mathrm{W}_n(k)[G]$-modules. To study these representations, we introduce a theory of differential operators over the Witt vectors for smooth $k$-schemes $X$, through a quasi-coherent sheaf of $\\mathrm{W}_n(k)$-algebras $\\mathcal{D}_{\\mathrm{W}_n("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06246","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/2506.06246/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":"2506.06246","created_at":"2026-07-05T11:17:28.092736+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.06246v1","created_at":"2026-07-05T11:17:28.092736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06246","created_at":"2026-07-05T11:17:28.092736+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFWFT7JWQHSS","created_at":"2026-07-05T11:17:28.092736+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFWFT7JWQHSSFKXX","created_at":"2026-07-05T11:17:28.092736+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFWFT7JW","created_at":"2026-07-05T11:17:28.092736+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/PFWFT7JWQHSSFKXXRZGXJANQII","json":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII.json","graph_json":"https://pith.science/api/pith-number/PFWFT7JWQHSSFKXXRZGXJANQII/graph.json","events_json":"https://pith.science/api/pith-number/PFWFT7JWQHSSFKXXRZGXJANQII/events.json","paper":"https://pith.science/paper/PFWFT7JW"},"agent_actions":{"view_html":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII","download_json":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII.json","view_paper":"https://pith.science/paper/PFWFT7JW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.06246&json=true","fetch_graph":"https://pith.science/api/pith-number/PFWFT7JWQHSSFKXXRZGXJANQII/graph.json","fetch_events":"https://pith.science/api/pith-number/PFWFT7JWQHSSFKXXRZGXJANQII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII/action/storage_attestation","attest_author":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII/action/author_attestation","sign_citation":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII/action/citation_signature","submit_replication":"https://pith.science/pith/PFWFT7JWQHSSFKXXRZGXJANQII/action/replication_record"}},"created_at":"2026-07-05T11:17:28.092736+00:00","updated_at":"2026-07-05T11:17:28.092736+00:00"}