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We prove that the system {V_l^ab} is also a rational strictly compatible system under some group theoretic conditions, e.g., when G_l' is connected and satisfies Hypothesis A for some prime l'. As an application, we prove that the Tate conjecture for abelian variety X/K is independent of l if the algebraic monodromy groups of the Gal"},"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":"1603.01283","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-03T21:14:40Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"bec6776abedb2241a68891fccd7e352448a5f74d1ee4fce9fcb9dd4d495091ea","abstract_canon_sha256":"126e287ff13bdaad03c1d2d3970c38f602b4d8c4a9923316427a814b9a39aa4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:20.029154Z","signature_b64":"C2R7VIZq2YG9MHP8aD2ub3OOalGYQ8YETS2i27bydsSn0zuO29k/0pE1MquaOwYaZui9AU5Xw03e9PDj/qNZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911d746f5440e02e54fc52d46dba12d5a522ec1c5b5d41feec2d7163a7327442","last_reissued_at":"2026-05-18T00:05:20.028660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:20.028660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The abelian part of a compatible system and l-independence of the Tate conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"Chun Yin Hui","submitted_at":"2016-03-03T21:14:40Z","abstract_excerpt":"Let K be a number field and {V_l} be a rational strictly compatible system of semisimple Galois representations of K arising from geometry. Let G_l and V_l^ab be respectively the algebraic monodromy group and the maximal abelian subrepresentation of V_l for all l. We prove that the system {V_l^ab} is also a rational strictly compatible system under some group theoretic conditions, e.g., when G_l' is connected and satisfies Hypothesis A for some prime l'. 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