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There are natural morphisms ${\\mathcal Q}(r,d) \\longrightarrow \\text{Sym}^d(X)$ and $\\text{Sym}^d(X) \\longrightarrow \\text{Pic}^d(X)$. We prove that both these morphisms induce isomorphism of Brauer groups if $d \\geq 2$. Consequently, the Brauer group of ${\\mathcal Q}(r,d)$ is identified with the Brauer group of $\\text{Pic}^d(X)$ if $d \\geq 2$."},"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":"1212.2081","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-10T14:46:37Z","cross_cats_sorted":[],"title_canon_sha256":"755ea3dcd3fe03167976135dcca7a299f232b090a8bd0f32b0bfd702d229c1c7","abstract_canon_sha256":"0be4426d0b132687cf3747da68aa6ef77f2bdc15c7d6183c6b926e8961eb5f3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:50.176099Z","signature_b64":"lZH3RCByR9SpuS5rfmIycr000nu6hhZlEnJj7cYQObB0sagV3ptk6xPpr0N/ZkhQTmAWvnjyvJyEmf1zp4W1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51bb1eeb4f9afb95226af34f666a6f7a965cf507f3a7274218f3aa2ec9623d08","last_reissued_at":"2026-05-18T02:18:50.175483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:50.175483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brauer Groups of Quot Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ajneet Dhillon, Indranil Biswas, Jacques Hurtubise","submitted_at":"2012-12-10T14:46:37Z","abstract_excerpt":"Let $X$ be an irreducible smooth complex projective curve. Let ${\\mathcal Q}(r,d)$ be the Quot scheme parametrizing all coherent subsheaves of ${\\mathcal O}^{\\oplus r}_X$ of rank $r$ and degree $-d$. There are natural morphisms ${\\mathcal Q}(r,d) \\longrightarrow \\text{Sym}^d(X)$ and $\\text{Sym}^d(X) \\longrightarrow \\text{Pic}^d(X)$. We prove that both these morphisms induce isomorphism of Brauer groups if $d \\geq 2$. Consequently, the Brauer group of ${\\mathcal Q}(r,d)$ is identified with the Brauer group of $\\text{Pic}^d(X)$ if $d \\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2081","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.2081","created_at":"2026-05-18T02:18:50.175576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2081v2","created_at":"2026-05-18T02:18:50.175576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2081","created_at":"2026-05-18T02:18:50.175576+00:00"},{"alias_kind":"pith_short_12","alias_value":"KG5R522PTL5Z","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KG5R522PTL5ZKITK","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KG5R522P","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK","json":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK.json","graph_json":"https://pith.science/api/pith-number/KG5R522PTL5ZKITK6NHWM2TPPK/graph.json","events_json":"https://pith.science/api/pith-number/KG5R522PTL5ZKITK6NHWM2TPPK/events.json","paper":"https://pith.science/paper/KG5R522P"},"agent_actions":{"view_html":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK","download_json":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK.json","view_paper":"https://pith.science/paper/KG5R522P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2081&json=true","fetch_graph":"https://pith.science/api/pith-number/KG5R522PTL5ZKITK6NHWM2TPPK/graph.json","fetch_events":"https://pith.science/api/pith-number/KG5R522PTL5ZKITK6NHWM2TPPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK/action/storage_attestation","attest_author":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK/action/author_attestation","sign_citation":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK/action/citation_signature","submit_replication":"https://pith.science/pith/KG5R522PTL5ZKITK6NHWM2TPPK/action/replication_record"}},"created_at":"2026-05-18T02:18:50.175576+00:00","updated_at":"2026-05-18T02:18:50.175576+00:00"}