{"paper":{"title":"Families of Group Actions, Generic Isotriviality, and Linearization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.RT","authors_text":"Hanspeter Kraft, Peter Russell","submitted_at":"2012-04-14T19:02:20Z","abstract_excerpt":"We prove a \"Generic Equivalence Theorem which says that two affine morphisms $p: S \\to Y$ and $q: T \\to Y$ of varieties with isomorphic (closed) fibers become isomorphic under a dominant etale base change $\\phi: U \\to Y$. A special case is the following result. Call a morphism $\\phi: X \\to Y$ a \"fibration with fiber $F$\" if $\\phi$ is flat and all fibers are (reduced and) isomorphic to $F$. Then an affine fibration with fiber $F$ admits an etale dominant morphism $\\mu: U \\to Y$ such that the pull-back is a trivial fiber bundle: $U\\times_Y X \\simeq U\\times F$. As an application we give short pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3196","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"}