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Assuming the Mumford-Tate conjecture, we formulate a conjecture (Conjecture 1.2) describing the largeness of the image of the absolute Galois group $G_K$ in $H(\\A_f)$ under the adelic Galois representation $\\rho_{\\A}: G_K -> \\Aut(V_{\\A})=\\GL_n(\\A_f)$, where $H$ is the Hodge group. The motivating example is a celebrated theorem of Serre, which asserts that if $X$ is an elliptic curve with"},"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":"1312.3812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-13T14:10:57Z","cross_cats_sorted":[],"title_canon_sha256":"eed6bf3c4fa220d0142bcf1b4160cc615885717979df98b4ffab4b90239c66c2","abstract_canon_sha256":"c65c8873bdd9d90383cd2fd9188d2d9777dac5f3c11464e4972250eb3d1ee875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:35.858276Z","signature_b64":"0LaQSpvhMV9IJ7oK6SDSLG42uDzSuyAB45RVlL9fpRiQNRQs2xEro1u4ZXN0nY7EaK4/+QiWmLJSIIB+z+RcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3615287994c52331c4979124f7810c358a2b1e7024927dc10d9fe559cdf82179","last_reissued_at":"2026-05-18T01:34:35.857781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:35.857781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adelic openness without the Mumford-Tate conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chun Yin Hui, Michael Larsen","submitted_at":"2013-12-13T14:10:57Z","abstract_excerpt":"Let $X$ be a non-singular projective variety over a number field $K$, $i$ a non-negative integer, and $V_{\\A}$, the etale cohomology of $\\bar X$ with coefficients in the ring of finite adeles $\\A_f$ over $\\Q$. Assuming the Mumford-Tate conjecture, we formulate a conjecture (Conjecture 1.2) describing the largeness of the image of the absolute Galois group $G_K$ in $H(\\A_f)$ under the adelic Galois representation $\\rho_{\\A}: G_K -> \\Aut(V_{\\A})=\\GL_n(\\A_f)$, where $H$ is the Hodge group. 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