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We consider the induced map X(K)-->Y(K), which is continuous for the topologies deduced from the valuation. Let I denote the image of this map.\n  We prove that if (K,v) is henselian and its completion is a separable extension, then:\n  - I is locally closed in Y(K);\n  - the induced surjection X(K)-->I is a principal bundle with group G(K) (also topologized by the valuation).","authors_text":"Laurent Moret-Bailly, Ofer Gabber, Philippe Gille","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-25T08:53:45Z","title":"Fibr\\'es principaux sur les corps valu\\'es hens\\'eliens"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6430","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8c7ddfa15578ec1e58ba13c363a051fe7e254b2cf5b0e4dd1b772fb0b7953b19","target":"record","created_at":"2026-05-18T02:47:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f982447da6ffe0dbeef6c14bef88b16a030343e99f73f99dbe820310edfcf63b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-25T08:53:45Z","title_canon_sha256":"6ccb93c05475588113e329b9ecf7554f183a288ec5748a0690fee7513b51f6ea"},"schema_version":"1.0","source":{"id":"1309.6430","kind":"arxiv","version":3}},"canonical_sha256":"92097ce2774f1832340cf8918c737b080db1314a9a0acb0c41ff54fcbda97eb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92097ce2774f1832340cf8918c737b080db1314a9a0acb0c41ff54fcbda97eb8","first_computed_at":"2026-05-18T02:47:05.702835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:05.702835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t3T5y8SPCnHdVfz0gex/vc1+ptxe1Y66u5yDw0H90dmwRI3kYli0xe8tjnJu2fzZDUgDEfMZlHkmP2PXotkLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:05.703436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6430","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c7ddfa15578ec1e58ba13c363a051fe7e254b2cf5b0e4dd1b772fb0b7953b19","sha256:58e331808cb68d932971c9b5110152a87d7dd1ed43cae244253eeb44f401b2d2"],"state_sha256":"0cb045f018b82cb1fbe5d0b9723494c0de4759c4605b139b7f489c7d093d45d8"}