{"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. The motivating example is a celebrated theorem of Serre, which asserts that if $X$ is an elliptic curve with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3812","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"}