{"paper":{"title":"Subgroup structure of fundamental groups in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lior Bary-Soroker, Manish Kumar","submitted_at":"2011-06-29T17:07:37Z","abstract_excerpt":"Let $\\Pi$ be the \\'etale fundamental group of a smooth affine curve over an algebraically closed field of characteristic $p>0$. We establish a criterion for profinite freeness of closed subgroups of $\\Pi$. Roughly speaking, if a closed subgroup of $\\Pi$ is \"captured\" between two normal subgroups, then it is free, provided it contains most of the open subgroups of index $p$. In the proof we establish a strong version of \"almost $\\omega$-freeness\" of $\\Pi$ and then apply the Haran-Shapiro induction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6004","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"}