{"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"}