{"paper":{"title":"Specialization results in Galois theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Fran\\c{c}ois Legrand, Pierre D\\`ebes","submitted_at":"2011-06-30T09:07:16Z","abstract_excerpt":"The paper has three main applications. The first one is this Hilbert-Grunwald statement. If $f:X\\rightarrow \\Pp^1$ is a degree $n$ $\\Qq$-cover with monodromy group $S_n$ over $\\bar\\Qq$, and finitely many suitably big primes $p$ are given with partitions $\\{d_{p,1},..., d_{p,s_p}\\}$ of $n$, there exist infinitely many specializations of $f$ at points $t_0\\in \\Qq$ that are degree $n$ field extensions with residue degrees $d_{p,1},..., d_{p,s_p}$ at each prescribed prime $p$. The second one provides a description of the se-pa-ra-ble closure of a PAC field $k$ of characteristic $p\\not=2$: it is ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6151","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"}