{"paper":{"title":"Specialization of monodromy group and l-independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chun Yin Hui","submitted_at":"2011-10-21T16:35:24Z","abstract_excerpt":"Let $E$ be an abelian scheme over a geometrically connected variety $X$ defined over $k$, a finitely generated field over $\\mathbb{Q}$. Let $\\eta$ be the generic point of $X$ and $x\\in X$ a closed point. If $\\mathfrak{g}_l$ and $(\\mathfrak{g}_l)_x$ are the Lie algebras of the $l$-adic Galois representations for abelian varieties $E_{\\eta}$ and $E_x$, then $(\\mathfrak{g}_l)_x$ is embedded in $\\mathfrak{g}_l$ by specialization. We prove that the set $\\{x\\in X$ closed point $| (\\mathfrak{g}_l)_x\\subsetneq \\mathfrak{g}_l\\}$ is independent of $l$ and confirm Conjecture 5.5 in [2]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4836","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"}