{"paper":{"title":"Reductive Shafarevich Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Katsutoshi Yamanoi, Ludmil Katzarkov, Ya Deng","submitted_at":"2023-06-05T17:48:31Z","abstract_excerpt":"In this paper, we prove the holomorphic convexity of the covering of a complex projective {normal} variety $X$, which corresponds to the intersection of kernels of reductive representations $\\rho:\\pi_1(X)\\to {\\rm GL}_{N}(\\mathbb{C})$, therefore answering a question by Eyssidieux, Katzarkov, Pantev, and Ramachandran in 2012. It is worth noting that Eyssidieux had previously proven this result in 2004 when $X$ is smooth. While our approach follows the general strategy employed in Eyssidieux's proof, it introduces several improvements and simplifications. Notably, it avoids the necessity of using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03070","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.03070/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"}