{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YSA5TXBBQ6KV7SL7VMPMB7QIKO","short_pith_number":"pith:YSA5TXBB","schema_version":"1.0","canonical_sha256":"c481d9dc2187955fc97fab1ec0fe08539c090a696a07642e1bbc3841d3ab8cca","source":{"kind":"arxiv","id":"1703.06235","version":1},"attestation_state":"computed","paper":{"title":"On the local-global divisibility over ${\\rm GL}_2$-type varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florence Gillibert, Gabriele Ranieri","submitted_at":"2017-03-18T02:37:50Z","abstract_excerpt":"Let $k$ be a number field and let ${\\mathcal{A}}$ be a ${\\rm GL}_2$-type variety defined over $k$ of dimension $d$. We show that for every prime number $p$ satisfying certain conditions (see Theorem 2), if the local-global divisibility principle by a power of $p$ does not hold for ${\\mathcal{A}}$ over $k$, then there exists a cyclic extension $\\widetilde{k}$ of $k$ of degree bounded by a constant depending on $d$ such that ${\\mathcal{A}}$ is $\\widetilde{k}$-isogenous to a ${\\rm GL}_2$-type variety defined over $\\widetilde{k}$ that admits a $\\widetilde{k}$-rational point of order $p$. Moreover,"},"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":"1703.06235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-18T02:37:50Z","cross_cats_sorted":[],"title_canon_sha256":"f9969b4927fec989bcdafd4a9f4137c56506b6c1f1c9496172269fd1cd28c7e7","abstract_canon_sha256":"54290c50c1c21899736ea592ce8ec373ff73a3154bf78c06cd5db0297b5f1c70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:23.547890Z","signature_b64":"w0dAWidr+bvDqk+Es27M5cTyhKT0V5dcxOdFe0hLybhB/veHZD6YGEbFS/pIEb8NQ96NQyk9IBqSnn9XHx8KBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c481d9dc2187955fc97fab1ec0fe08539c090a696a07642e1bbc3841d3ab8cca","last_reissued_at":"2026-05-18T00:48:23.547213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:23.547213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the local-global divisibility over ${\\rm GL}_2$-type varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florence Gillibert, Gabriele Ranieri","submitted_at":"2017-03-18T02:37:50Z","abstract_excerpt":"Let $k$ be a number field and let ${\\mathcal{A}}$ be a ${\\rm GL}_2$-type variety defined over $k$ of dimension $d$. We show that for every prime number $p$ satisfying certain conditions (see Theorem 2), if the local-global divisibility principle by a power of $p$ does not hold for ${\\mathcal{A}}$ over $k$, then there exists a cyclic extension $\\widetilde{k}$ of $k$ of degree bounded by a constant depending on $d$ such that ${\\mathcal{A}}$ is $\\widetilde{k}$-isogenous to a ${\\rm GL}_2$-type variety defined over $\\widetilde{k}$ that admits a $\\widetilde{k}$-rational point of order $p$. Moreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06235","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":""},"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":"1703.06235","created_at":"2026-05-18T00:48:23.547324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06235v1","created_at":"2026-05-18T00:48:23.547324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06235","created_at":"2026-05-18T00:48:23.547324+00:00"},{"alias_kind":"pith_short_12","alias_value":"YSA5TXBBQ6KV","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YSA5TXBBQ6KV7SL7","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YSA5TXBB","created_at":"2026-05-18T12:31:56.362134+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/YSA5TXBBQ6KV7SL7VMPMB7QIKO","json":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO.json","graph_json":"https://pith.science/api/pith-number/YSA5TXBBQ6KV7SL7VMPMB7QIKO/graph.json","events_json":"https://pith.science/api/pith-number/YSA5TXBBQ6KV7SL7VMPMB7QIKO/events.json","paper":"https://pith.science/paper/YSA5TXBB"},"agent_actions":{"view_html":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO","download_json":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO.json","view_paper":"https://pith.science/paper/YSA5TXBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06235&json=true","fetch_graph":"https://pith.science/api/pith-number/YSA5TXBBQ6KV7SL7VMPMB7QIKO/graph.json","fetch_events":"https://pith.science/api/pith-number/YSA5TXBBQ6KV7SL7VMPMB7QIKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO/action/storage_attestation","attest_author":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO/action/author_attestation","sign_citation":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO/action/citation_signature","submit_replication":"https://pith.science/pith/YSA5TXBBQ6KV7SL7VMPMB7QIKO/action/replication_record"}},"created_at":"2026-05-18T00:48:23.547324+00:00","updated_at":"2026-05-18T00:48:23.547324+00:00"}