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For a field $k$ we denote by $k_{\\mathrm{ab}}$ its maximal abelian Galois extension. We prove that there exist finite Galois extensions $k/\\mathbb{Q}$ and $F/K$ such that the restricted family of representations $(\\rho_\\ell|\\mathrm{Gal}(k_{\\mathrm{ab}} F))_\\ell$ is group theoretically independent in the"},"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":"1701.04757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-17T16:47:18Z","cross_cats_sorted":[],"title_canon_sha256":"226ae930d274b905bd095027bac3929e954eb2ae9c4238aac352d3150d18fdeb","abstract_canon_sha256":"0cb53fb868680793fd4d09e52563aa5bead58cdc18fba637a05e0af6c660e981"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:35.168917Z","signature_b64":"VHAlzAdNTyL15cpJ+mtUj0+za3NdtvopeqT13hVq4vDFv3I/YwsPN0Rwit7RrX9/0UvlRZkYxM2Rfc9Gzw/cAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27aa3bbe35fb966f60d36920929c07b455385b257e74abbba5efc26557ea71b6","last_reissued_at":"2026-05-18T00:52:35.168461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:35.168461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group theoretical independence of $\\ell$-adic Galois representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sebastian Petersen","submitted_at":"2017-01-17T16:47:18Z","abstract_excerpt":"Let $K/\\mathbb{Q}$ be a finitely generated field of characteristic zero and $X/K$ a smooth projective variety. Fix $q\\in\\mathbb{N}$. For every prime number $\\ell$ let $\\rho_\\ell$ be the representation of $\\mathrm{Gal}(K)$ on the \\'etale cohomology group $H^q(X_{\\overline{K}}, \\mathbb{Q}_\\ell)$. For a field $k$ we denote by $k_{\\mathrm{ab}}$ its maximal abelian Galois extension. We prove that there exist finite Galois extensions $k/\\mathbb{Q}$ and $F/K$ such that the restricted family of representations $(\\rho_\\ell|\\mathrm{Gal}(k_{\\mathrm{ab}} F))_\\ell$ is group theoretically independent in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04757","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":"1701.04757","created_at":"2026-05-18T00:52:35.168538+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.04757v1","created_at":"2026-05-18T00:52:35.168538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04757","created_at":"2026-05-18T00:52:35.168538+00:00"},{"alias_kind":"pith_short_12","alias_value":"E6VDXPRV7OLG","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"E6VDXPRV7OLG6YGT","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"E6VDXPRV","created_at":"2026-05-18T12:31:12.930513+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/E6VDXPRV7OLG6YGTNEQJFHAHWR","json":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR.json","graph_json":"https://pith.science/api/pith-number/E6VDXPRV7OLG6YGTNEQJFHAHWR/graph.json","events_json":"https://pith.science/api/pith-number/E6VDXPRV7OLG6YGTNEQJFHAHWR/events.json","paper":"https://pith.science/paper/E6VDXPRV"},"agent_actions":{"view_html":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR","download_json":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR.json","view_paper":"https://pith.science/paper/E6VDXPRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.04757&json=true","fetch_graph":"https://pith.science/api/pith-number/E6VDXPRV7OLG6YGTNEQJFHAHWR/graph.json","fetch_events":"https://pith.science/api/pith-number/E6VDXPRV7OLG6YGTNEQJFHAHWR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR/action/storage_attestation","attest_author":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR/action/author_attestation","sign_citation":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR/action/citation_signature","submit_replication":"https://pith.science/pith/E6VDXPRV7OLG6YGTNEQJFHAHWR/action/replication_record"}},"created_at":"2026-05-18T00:52:35.168538+00:00","updated_at":"2026-05-18T00:52:35.168538+00:00"}