{"paper":{"title":"Galois realizations with inertia groups of order two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Rabayev, Jack Sonn, Joachim Koenig","submitted_at":"2017-01-08T15:20:30Z","abstract_excerpt":"There are several variants of the inverse Galois problem which involve restrictions on ramification. In this paper we give sufficient conditions that a given finite group $G$ occurs infinitely often as a Galois group over the rationals $\\mathbb Q$ with all nontrivial inertia groups of order $2$. Notably any such realization of $G$ can be translated up to a quadratic field over which the corresponding realization of $G$ is unramified.\n  The sufficient conditions are imposed on a parametric polynomial with Galois group $G$--if such a polynomial is available--and the infinitely many realizations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01969","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":""},"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"}