{"paper":{"title":"A uniform open image theorem for l-adic representations in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Emiliano Ambrosi","submitted_at":"2017-11-16T15:16:44Z","abstract_excerpt":"Let $k$ be a finitely generated field of characteristic $p > 0$ and $\\ell$ a prime. Let $X$ be a smooth, separated, geometrically connected curve of finite type over $k$ and $\\rho: \\pi_1(X)\\rightarrow GL_r(\\mathbb Z_{\\ell})$ a continuous representation of the \\etale fundamental group of $X$ with image $G$. Any $k$-rational point $x:Spec(k)\\rightarrow X$ induces a local representation $\\rho_x: \\pi_1(Spec(k)) \\rightarrow \\pi_1(X) \\rightarrow GL_r(\\mathbb Z_{\\ell})$ with image $G_x$. The goal of this paper is to study how $G_x$ varies with $x\\in X(k)$. In particular we prove that if $\\ell\\neq p$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06132","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"}