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Let $G$ be a finite solvable $K$-group scheme and assume that either $|G|=p^n$ or $G$ has a normal series of length 2. We prove that every quotient pointed $G$-torsor over the generic fiber $X_{\\eta}$ of $X$ can be extended to a torsor over $X$ after eventually extending scalars and after eventually blowing up $X$ at a closed subscheme of its s"},"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":"1012.1782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-08T15:19:46Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"b8c4904646e986b2e91dca667f8c5af3eac8b84971106e48e48a9d20c8e71f2b","abstract_canon_sha256":"b22a1f7f76d3a6085e07041e55700b0c3da2d667fd45ca56b0264bf8060f70c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.366495Z","signature_b64":"myCLlfaDFoW4Z8yskGAxGkQK7rNGQozTIMAvrQojg7oKeE1HDjFlRqCEHbClcxbP+wY1m70FuQNUEw+vjNcHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ad97f008a9505cfa681cef902190eaa136f4d7e1ec27572ff2892ca784fed0b","last_reissued_at":"2026-05-18T03:45:23.366019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.366019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extention of Finite Solvable Torsors over a Curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Marco Antei","submitted_at":"2010-12-08T15:19:46Z","abstract_excerpt":"Let $R$ be a discrete valuation ring with fraction field $K$ and with algebraically closed residue field of positive characteristic $p$. 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