{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FD3DBARTSER6QIIUI2PE6NMOYH","short_pith_number":"pith:FD3DBART","schema_version":"1.0","canonical_sha256":"28f63082339123e82114469e4f358ec1f68dbdf8422f79e57538b37de8652b9f","source":{"kind":"arxiv","id":"1703.10237","version":2},"attestation_state":"computed","paper":{"title":"Graded analogues of one-parameter subgroups and applications to the cohomology of $GL_{m|n(r)}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Christopher M. Drupieski, Jonathan R. Kujawa","submitted_at":"2017-03-29T20:25:57Z","abstract_excerpt":"We introduce a family $\\mathbb{M}_{r;f,\\eta}$ of infinitesimal supergroup schemes, which we call multiparameter supergroups, that generalize the infinitesimal Frobenius kernels $\\mathbb{G}_{a(r)}$ of the additive group scheme $\\mathbb{G}_{a}$. Then, following the approach of Suslin, Friedlander, and Bendel, we use functor cohomology to define characteristic extension classes for the general linear supergroup $GL_{m|n}$, and we calculate how these classes restrict along homomorphisms $\\rho: \\mathbb{M}_{r;f,\\eta} \\rightarrow GL_{m|n}.$ Finally, we apply our calculations to describe (up to a fini"},"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":"1703.10237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-29T20:25:57Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f8b889addb1bb7a1b453aef90660f3efc04e7c74f5e9ee4857bed44935202698","abstract_canon_sha256":"2a001e7fe54ce8f0f380bd2510330f2c845666aebbe37df242e1217df622566d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:47.287899Z","signature_b64":"F3SKcD/jACvOEJ+nIGAlJR8V+lqh1tf0jOSyUz83nZEMTq79wa8xdDdWilnTIL/m32y1haOL7mxuAEubKt0CDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28f63082339123e82114469e4f358ec1f68dbdf8422f79e57538b37de8652b9f","last_reissued_at":"2026-05-17T23:50:47.287101Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:47.287101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graded analogues of one-parameter subgroups and applications to the cohomology of $GL_{m|n(r)}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Christopher M. Drupieski, Jonathan R. Kujawa","submitted_at":"2017-03-29T20:25:57Z","abstract_excerpt":"We introduce a family $\\mathbb{M}_{r;f,\\eta}$ of infinitesimal supergroup schemes, which we call multiparameter supergroups, that generalize the infinitesimal Frobenius kernels $\\mathbb{G}_{a(r)}$ of the additive group scheme $\\mathbb{G}_{a}$. Then, following the approach of Suslin, Friedlander, and Bendel, we use functor cohomology to define characteristic extension classes for the general linear supergroup $GL_{m|n}$, and we calculate how these classes restrict along homomorphisms $\\rho: \\mathbb{M}_{r;f,\\eta} \\rightarrow GL_{m|n}.$ Finally, we apply our calculations to describe (up to a fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10237","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":"1703.10237","created_at":"2026-05-17T23:50:47.287215+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10237v2","created_at":"2026-05-17T23:50:47.287215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10237","created_at":"2026-05-17T23:50:47.287215+00:00"},{"alias_kind":"pith_short_12","alias_value":"FD3DBARTSER6","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FD3DBARTSER6QIIU","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FD3DBART","created_at":"2026-05-18T12:31:15.632608+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/FD3DBARTSER6QIIUI2PE6NMOYH","json":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH.json","graph_json":"https://pith.science/api/pith-number/FD3DBARTSER6QIIUI2PE6NMOYH/graph.json","events_json":"https://pith.science/api/pith-number/FD3DBARTSER6QIIUI2PE6NMOYH/events.json","paper":"https://pith.science/paper/FD3DBART"},"agent_actions":{"view_html":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH","download_json":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH.json","view_paper":"https://pith.science/paper/FD3DBART","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10237&json=true","fetch_graph":"https://pith.science/api/pith-number/FD3DBARTSER6QIIUI2PE6NMOYH/graph.json","fetch_events":"https://pith.science/api/pith-number/FD3DBARTSER6QIIUI2PE6NMOYH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH/action/storage_attestation","attest_author":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH/action/author_attestation","sign_citation":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH/action/citation_signature","submit_replication":"https://pith.science/pith/FD3DBARTSER6QIIUI2PE6NMOYH/action/replication_record"}},"created_at":"2026-05-17T23:50:47.287215+00:00","updated_at":"2026-05-17T23:50:47.287215+00:00"}