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If $\\mathfrak{g}_l$ and $(\\mathfrak{g}_l)_x$ are the Lie algebras of the $l$-adic Galois representations for abelian varieties $E_{\\eta}$ and $E_x$, then $(\\mathfrak{g}_l)_x$ is embedded in $\\mathfrak{g}_l$ by specialization. We prove that the set $\\{x\\in X$ closed point $| (\\mathfrak{g}_l)_x\\subsetneq \\mathfrak{g}_l\\}$ is independent of $l$ and confirm Conjecture 5.5 in [2]."},"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":"1110.4836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-21T16:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"291f9d93eef2434dcdfda54ccbac80e37db48fd1465fce5f5c22c6c405a1035f","abstract_canon_sha256":"9ee142bb4934a22d3de518ff019f4eb10f75d492a57f223470ead328e5bfcaaa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:23.665304Z","signature_b64":"bo+zui6UJcGqUAKG2pmNMmVxYqY8muHUgN3k6C2hzls3QKImd6lKfepjrwNbwnZoAXgz32/28D6baoI2uREaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a37b458c164c38a3ed75e59fce3dad687cf7b699be1c17f3cea74911af06c988","last_reissued_at":"2026-05-18T04:08:23.664793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:23.664793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Specialization of monodromy group and l-independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chun Yin Hui","submitted_at":"2011-10-21T16:35:24Z","abstract_excerpt":"Let $E$ be an abelian scheme over a geometrically connected variety $X$ defined over $k$, a finitely generated field over $\\mathbb{Q}$. Let $\\eta$ be the generic point of $X$ and $x\\in X$ a closed point. If $\\mathfrak{g}_l$ and $(\\mathfrak{g}_l)_x$ are the Lie algebras of the $l$-adic Galois representations for abelian varieties $E_{\\eta}$ and $E_x$, then $(\\mathfrak{g}_l)_x$ is embedded in $\\mathfrak{g}_l$ by specialization. We prove that the set $\\{x\\in X$ closed point $| (\\mathfrak{g}_l)_x\\subsetneq \\mathfrak{g}_l\\}$ is independent of $l$ and confirm Conjecture 5.5 in [2]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4836","kind":"arxiv","version":2},"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":"1110.4836","created_at":"2026-05-18T04:08:23.664883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.4836v2","created_at":"2026-05-18T04:08:23.664883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4836","created_at":"2026-05-18T04:08:23.664883+00:00"},{"alias_kind":"pith_short_12","alias_value":"UN5ULDAWJQ4K","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UN5ULDAWJQ4KH3LV","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UN5ULDAW","created_at":"2026-05-18T12:26:42.757692+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/UN5ULDAWJQ4KH3LV4WP44PNNNB","json":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB.json","graph_json":"https://pith.science/api/pith-number/UN5ULDAWJQ4KH3LV4WP44PNNNB/graph.json","events_json":"https://pith.science/api/pith-number/UN5ULDAWJQ4KH3LV4WP44PNNNB/events.json","paper":"https://pith.science/paper/UN5ULDAW"},"agent_actions":{"view_html":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB","download_json":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB.json","view_paper":"https://pith.science/paper/UN5ULDAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.4836&json=true","fetch_graph":"https://pith.science/api/pith-number/UN5ULDAWJQ4KH3LV4WP44PNNNB/graph.json","fetch_events":"https://pith.science/api/pith-number/UN5ULDAWJQ4KH3LV4WP44PNNNB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB/action/storage_attestation","attest_author":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB/action/author_attestation","sign_citation":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB/action/citation_signature","submit_replication":"https://pith.science/pith/UN5ULDAWJQ4KH3LV4WP44PNNNB/action/replication_record"}},"created_at":"2026-05-18T04:08:23.664883+00:00","updated_at":"2026-05-18T04:08:23.664883+00:00"}