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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.3196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-14T19:02:20Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"c97c61c20ff46561bbfb5f963929cb2ee9365e91a05b76448992a07acaa8d318","abstract_canon_sha256":"73c03b786c18f7d5fc721e0e9a5c5ac8cb12a1764d3fdae46eac0c4d98dd9d0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.298092Z","signature_b64":"FaQAEUQt0ge/Zxvo9EhJeQiAy3OZIQbVLqfJDahQ4wNsDo6atMmLFiaSpk6OYwrhdEO7uAIKqRv9DTsIpLTCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa9e6b644701ca191403f4e27c37e414bd582c23c6a43634d87a153d58b9ce98","last_reissued_at":"2026-05-18T03:57:52.297512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.297512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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: $U\\times_Y X \\simeq U\\times F$. 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