{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:K2WNXRNDSCMGVRQ7REOXIWZ5FH","short_pith_number":"pith:K2WNXRND","schema_version":"1.0","canonical_sha256":"56acdbc5a390986ac61f891d745b3d29d9bc9efe79dbec87261c78a5378f85aa","source":{"kind":"arxiv","id":"1705.10187","version":2},"attestation_state":"computed","paper":{"title":"The Frobenius morphism on flag varieties, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Samokhin","submitted_at":"2017-05-29T13:56:30Z","abstract_excerpt":"In this paper, which is the sequel to arXiv:1410.3742, we study the Frobenius pushforward of the structure sheaf on the adjoint varieties in type ${\\bf A}_3$ and ${\\bf A}_4$. We show that this pushforward sheaf decomposes into a direct sum of indecomposable bundles and explicitly determine this set that does not depend of the characteristic. In accordance with the results of arXiv:0707.0913, this set forms a strong full exceptional collection in the derived category of coherent sheaves. These computations lead to a natural conjectural answer in the general case that we state at the end."},"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":"1705.10187","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-29T13:56:30Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e75fc6daf300d05c20b8022a466db2e1c321cf0343d27dd2bf174d72261c87b3","abstract_canon_sha256":"0601f7ecb2c0b07adf9735be932bc6ccce56b9616c308bdade3e0f93c5a5965d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:29.894274Z","signature_b64":"UptPFrjgVlt3EMq+s2Uo+alVT75HW1xGYexAZWTKbMgFkc9bX1GoXBWzcWQLbLVKzkaVqyrzW8omTUjneOmMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56acdbc5a390986ac61f891d745b3d29d9bc9efe79dbec87261c78a5378f85aa","last_reissued_at":"2026-05-18T00:40:29.893854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:29.893854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Frobenius morphism on flag varieties, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Samokhin","submitted_at":"2017-05-29T13:56:30Z","abstract_excerpt":"In this paper, which is the sequel to arXiv:1410.3742, we study the Frobenius pushforward of the structure sheaf on the adjoint varieties in type ${\\bf A}_3$ and ${\\bf A}_4$. We show that this pushforward sheaf decomposes into a direct sum of indecomposable bundles and explicitly determine this set that does not depend of the characteristic. In accordance with the results of arXiv:0707.0913, this set forms a strong full exceptional collection in the derived category of coherent sheaves. These computations lead to a natural conjectural answer in the general case that we state at the end."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10187","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":"1705.10187","created_at":"2026-05-18T00:40:29.893919+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.10187v2","created_at":"2026-05-18T00:40:29.893919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10187","created_at":"2026-05-18T00:40:29.893919+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2WNXRNDSCMG","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2WNXRNDSCMGVRQ7","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2WNXRND","created_at":"2026-05-18T12:31:24.725408+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/K2WNXRNDSCMGVRQ7REOXIWZ5FH","json":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH.json","graph_json":"https://pith.science/api/pith-number/K2WNXRNDSCMGVRQ7REOXIWZ5FH/graph.json","events_json":"https://pith.science/api/pith-number/K2WNXRNDSCMGVRQ7REOXIWZ5FH/events.json","paper":"https://pith.science/paper/K2WNXRND"},"agent_actions":{"view_html":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH","download_json":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH.json","view_paper":"https://pith.science/paper/K2WNXRND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.10187&json=true","fetch_graph":"https://pith.science/api/pith-number/K2WNXRNDSCMGVRQ7REOXIWZ5FH/graph.json","fetch_events":"https://pith.science/api/pith-number/K2WNXRNDSCMGVRQ7REOXIWZ5FH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH/action/storage_attestation","attest_author":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH/action/author_attestation","sign_citation":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH/action/citation_signature","submit_replication":"https://pith.science/pith/K2WNXRNDSCMGVRQ7REOXIWZ5FH/action/replication_record"}},"created_at":"2026-05-18T00:40:29.893919+00:00","updated_at":"2026-05-18T00:40:29.893919+00:00"}