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Consider a fibration in torsors under $T$, i.e. a morphism $f: X \\to \\mathbb{P}^1_k$ from a smooth, projective $k$-variety $X$ to $\\mathbb{P}^1_k$ such that the generic fibre $X_\\eta \\to \\eta$ is a smooth compactification of a principal homogeneous space under $T \\times_k \\eta$.\n  We study the Brauer-Manin obstruction to the Hasse principle and weak approximation for $X$, under Schinzel's hypothesis, thereby generalizing recent work of Wei. Our results are unconditional if $k = \\mathbb{Q}$ and the non-split fibres of $f$ are defined over $\\"},"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":"1305.0756","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T15:49:46Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0298d3230e64664c14652706d833ab65ca3044d16723047e70a9f453cd78ad83","abstract_canon_sha256":"2dd3b391d3ed6dd7439aeb76f5f79b396239cda7a035e3fbc52a294454f99180"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.553306Z","signature_b64":"MLGHsxXRvErtJAQ1YB5hhqG+yvISghQeXU9xh6AweBUgom3FMZ4C4Ertxbpr7enPS+xvHQnywEyZzf9ozi4sCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7844bded80c0920ef4cbbdb4d0bfc4b24a08a72b09595e89ff4f515405b22c7c","last_reissued_at":"2026-05-17T23:53:17.552624Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.552624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Principes locaux-globaux pour certaines fibrations en torseurs sous un tore","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arne Smeets","submitted_at":"2013-05-03T15:49:46Z","abstract_excerpt":"Let $k$ be a number field and let $T$ be a $k$-torus. 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