{"paper":{"title":"Hyperbolicity and fundamental groups of complex quasi-projective varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Benoit Cadorel, Katsutoshi Yamanoi, Ya Deng","submitted_at":"2022-12-23T09:29:55Z","abstract_excerpt":"This paper investigates the relationship between the hyperbolicity of complex quasi-projective varieties $X$ and the (topological) fundamental group $\\pi_1(X)$ in the presence of a linear representation $\\varrho: \\pi_1(X) \\to {\\rm GL}_N(\\mathbb{C})$. We present our main results in three parts.\n  Firstly, we show that if $\\varrho$ is bigand the Zariski closure of $\\varrho(\\pi_1(X))$ semisimple, then for any $X^\\sigma:=X\\times_\\sigma\\mathbb{C}$ where $\\sigma\\in {\\rm Aut}(\\mathbb{C}/\\mathbb{Q})$, there exists a proper Zariski closed subset $Z \\subsetneqq X^\\sigma$ such that any closed irreducible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12225","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.12225/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}