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Let $R:={\\rm Zar}(X)(K)\\cap X)$ be the Zariski closure of the set of all $K$-rational points of $X$, endowed with its reduced induced structure. We prove that there is a projective variety $X_0$ over $k$ and a finite and surjective $K^{\\rm sep}$-morphism $X_{0,K^{\\rm sep}}\\to R_{K^{\\rm sep}}$, which is birational when ${\\rm char}(K)=0$."},"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":"1312.6008","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-20T16:15:50Z","cross_cats_sorted":[],"title_canon_sha256":"a8fcb74592d35755c91e8dd3531e865f29a4eb84ed28d1d66f140137e1051303","abstract_canon_sha256":"2b9ff8cdf5b9c2ac25a910688e3eedac955b6de6343b4939bc1da88a28be39b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:46.845623Z","signature_b64":"yWb6jK9UpVoCNjZinRULtOpVkJNEjWqBUf3Ww40Ak04KZWQZM4BBT/ICL2SD4aKvFvgKxH0A9GcYlxIhR4xIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74e9c59fc36f60f27426a1df01c492bfbd7fc684d6fdeb192ac894efdd94e356","last_reissued_at":"2026-05-18T00:41:46.845088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:46.845088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational points of varieties with ample cotangent bundle over function fields of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Damian R\\\"ossler, Henri Gillet","submitted_at":"2013-12-20T16:15:50Z","abstract_excerpt":"Let $K$ be the function field of a smooth curve over an algebraically closed field $k$. Let $X$ be a scheme, which is smooth and projective over $K$. Suppose that the cotangent bundle $\\Omega_{X/K}$ is ample. Let $R:={\\rm Zar}(X)(K)\\cap X)$ be the Zariski closure of the set of all $K$-rational points of $X$, endowed with its reduced induced structure. We prove that there is a projective variety $X_0$ over $k$ and a finite and surjective $K^{\\rm sep}$-morphism $X_{0,K^{\\rm sep}}\\to R_{K^{\\rm sep}}$, which is birational when ${\\rm char}(K)=0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6008","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":"1312.6008","created_at":"2026-05-18T00:41:46.845162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.6008v3","created_at":"2026-05-18T00:41:46.845162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6008","created_at":"2026-05-18T00:41:46.845162+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTU4LH6DN5QP","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTU4LH6DN5QPE5BG","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTU4LH6D","created_at":"2026-05-18T12:27:54.935989+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/OTU4LH6DN5QPE5BGUHPQDRESX6","json":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6.json","graph_json":"https://pith.science/api/pith-number/OTU4LH6DN5QPE5BGUHPQDRESX6/graph.json","events_json":"https://pith.science/api/pith-number/OTU4LH6DN5QPE5BGUHPQDRESX6/events.json","paper":"https://pith.science/paper/OTU4LH6D"},"agent_actions":{"view_html":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6","download_json":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6.json","view_paper":"https://pith.science/paper/OTU4LH6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.6008&json=true","fetch_graph":"https://pith.science/api/pith-number/OTU4LH6DN5QPE5BGUHPQDRESX6/graph.json","fetch_events":"https://pith.science/api/pith-number/OTU4LH6DN5QPE5BGUHPQDRESX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6/action/storage_attestation","attest_author":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6/action/author_attestation","sign_citation":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6/action/citation_signature","submit_replication":"https://pith.science/pith/OTU4LH6DN5QPE5BGUHPQDRESX6/action/replication_record"}},"created_at":"2026-05-18T00:41:46.845162+00:00","updated_at":"2026-05-18T00:41:46.845162+00:00"}