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We show that the natural homomorphism determined by the second Drinfeld covering from the group of characters of $(\\mathbb{F}, +)$ to $\\text{Pic}(\\Sigma^1)[p]$ is injective. In particular, $\\text{Pic}(\\Sigma^1)[p] \\neq 0$. We also show that all vector bundles on $\\Omega^1$ are trivial, which e"},"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":"2307.12942","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2023-07-24T17:14:44Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"e50305b38102d3198e195edf4bff70b0e542af20570dfa05acf43d2ef79807a1","abstract_canon_sha256":"94fc71134c64ae9169289597397e33bc63c52f3575da39abd0143ba07d771a1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T14:03:16.770016Z","signature_b64":"bz+VPGO16y77iabhGgv6SjUXL7Ya31Tu55wYSxp1Phf12cMTjkkuH2tPF6W/VZ1HJu6XUnJKyhZeB5F/jnUTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8465092b0f2ea628b0b2f71647f1e604ed41f74ab225f714cb1d006efb4b5324","last_reissued_at":"2026-05-20T14:03:16.769541Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T14:03:16.769541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Line Bundles on The First Drinfeld Covering","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.RT","authors_text":"James Taylor","submitted_at":"2023-07-24T17:14:44Z","abstract_excerpt":"Let $\\Omega^d$ be the $d$-dimensional Drinfeld symmetric space for a finite extension $F$ of $\\mathbb{Q}_p$. Let $\\Sigma^1$ be a geometrically connected component of the first Drinfeld covering of $\\Omega^d$ and let $\\mathbb{F}$ be the residue field of the unique degree $d+1$ unramified extension of $F$. We show that the natural homomorphism determined by the second Drinfeld covering from the group of characters of $(\\mathbb{F}, +)$ to $\\text{Pic}(\\Sigma^1)[p]$ is injective. In particular, $\\text{Pic}(\\Sigma^1)[p] \\neq 0$. We also show that all vector bundles on $\\Omega^1$ are trivial, which e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.12942","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.12942/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":"2307.12942","created_at":"2026-05-20T14:03:16.769611+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.12942v3","created_at":"2026-05-20T14:03:16.769611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.12942","created_at":"2026-05-20T14:03:16.769611+00:00"},{"alias_kind":"pith_short_12","alias_value":"QRSQSKYPF2TC","created_at":"2026-05-20T14:03:16.769611+00:00"},{"alias_kind":"pith_short_16","alias_value":"QRSQSKYPF2TCRMFS","created_at":"2026-05-20T14:03:16.769611+00:00"},{"alias_kind":"pith_short_8","alias_value":"QRSQSKYP","created_at":"2026-05-20T14:03:16.769611+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/QRSQSKYPF2TCRMFS64LEP4PGAT","json":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT.json","graph_json":"https://pith.science/api/pith-number/QRSQSKYPF2TCRMFS64LEP4PGAT/graph.json","events_json":"https://pith.science/api/pith-number/QRSQSKYPF2TCRMFS64LEP4PGAT/events.json","paper":"https://pith.science/paper/QRSQSKYP"},"agent_actions":{"view_html":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT","download_json":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT.json","view_paper":"https://pith.science/paper/QRSQSKYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.12942&json=true","fetch_graph":"https://pith.science/api/pith-number/QRSQSKYPF2TCRMFS64LEP4PGAT/graph.json","fetch_events":"https://pith.science/api/pith-number/QRSQSKYPF2TCRMFS64LEP4PGAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT/action/storage_attestation","attest_author":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT/action/author_attestation","sign_citation":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT/action/citation_signature","submit_replication":"https://pith.science/pith/QRSQSKYPF2TCRMFS64LEP4PGAT/action/replication_record"}},"created_at":"2026-05-20T14:03:16.769611+00:00","updated_at":"2026-05-20T14:03:16.769611+00:00"}