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We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.\n  If the regular local ring R contains an infinite field this result is proved in [FP]. Thus the conjecture is true for regular local rings containing a field."},"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":"1707.01767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-05T10:05:04Z","cross_cats_sorted":[],"title_canon_sha256":"dd2d0f8a1644115f0ad4295f873cf096a7c1771c78ccd796613af29928869af1","abstract_canon_sha256":"3d438a58957b80647a08669d2dcc15b268bbcbe172c5f13425e8c077b1c51851"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:47.520536Z","signature_b64":"dnHQKSfMIwYvt4i2FuP6pvCg9QVJ6myBkFLgOTETjuUqi1c5Kbp1+lsit8HflD0T8TZ8ARleb1A1HCdvwXOzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe6560961bdb5964e7139eef684dd0aba2eafd0a77dd1c12f58f514205de8af2","last_reissued_at":"2026-05-18T00:40:47.519846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:47.519846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of Grothendieck--Serre conjecture on principal bundles over regular local rings containing a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Panin","submitted_at":"2017-07-05T10:05:04Z","abstract_excerpt":"Let R be a regular local ring, containing a finite field. 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