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We prove Pic(M_{r,L}^{ss}) = Z, identify the ample generator, and deduce that M_{r,L}^{ss} is locally factorial. In characteristic zero, this has already been proved by Dr\\'{e}zet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive caracteristic."},"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":"1204.4418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-19T17:37:43Z","cross_cats_sorted":[],"title_canon_sha256":"c4445e89f0e208df6e74154b5e0e7d70add47610bbb7ec791bfef7a05e05323b","abstract_canon_sha256":"74e3a3b68a6390ca96193abc4d0a7333145abfc4b6588215e5f61af0cb4faeca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:27.555578Z","signature_b64":"AWlbHc5aE6jz/oGKsScK0FyOSMhwQ9WlxWU32DNjLzRBVCbuTlYTDGinzZ+5o9XyVTx4yL+CJReTxLpd9MuTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9e0f06dd577ee176530668c46810d97b0923c9b3e00a33ff7c18e5fb41359f4","last_reissued_at":"2026-05-18T03:57:27.554942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:27.554942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Picard group of a coarse moduli space of vector bundles in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Norbert Hoffmann","submitted_at":"2012-04-19T17:37:43Z","abstract_excerpt":"Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M_{r,L}^{ss} denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M_{r,L}^{ss}) = Z, identify the ample generator, and deduce that M_{r,L}^{ss} is locally factorial. In characteristic zero, this has already been proved by Dr\\'{e}zet and Narasimhan. 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