{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GZ2O4TUOCAUEM4NIA2AL655TVG","short_pith_number":"pith:GZ2O4TUO","schema_version":"1.0","canonical_sha256":"3674ee4e8e10284671a80680bf77b3a98de3d54b3a5d1fbccd49a77852e33332","source":{"kind":"arxiv","id":"2412.15112","version":4},"attestation_state":"computed","paper":{"title":"Homology of Steinberg algebras","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GR","math.OA","math.RA"],"primary_cat":"math.KT","authors_text":"Devarshi Mukherjee, Guido Arnone, Guillermo Corti\\~nas","submitted_at":"2024-12-19T17:54:53Z","abstract_excerpt":"We study homological invariants of the Steinberg algebra $\\mathcal{A}_k(\\mathcal{G})$ of an ample groupoid $\\mathcal{G}$ over a commutative ring $k$. For $\\mathcal{G}$ principal or Hausdorff with ${\\mathcal{G}}^{\\rm{Iso}}\\setminus{\\mathcal{G}}^{(0)}$ discrete, we compute Hochschild and cyclic homology of $\\mathcal{A}_k(\\mathcal{G})$ in terms of groupoid homology. For any ample Hausdorff groupoid $\\mathcal{G}$, we find that $H_*(\\mathcal{G})$ is a direct summand of $HH_*(\\mathcal{A}_k(\\mathcal{G}))$; using this and the Dennis trace we obtain a map $\\overline{D}_*:K_*(\\mathcal{A}_k(\\mathcal{G}))"},"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":"2412.15112","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.KT","submitted_at":"2024-12-19T17:54:53Z","cross_cats_sorted":["math.GR","math.OA","math.RA"],"title_canon_sha256":"235ef0e949f122c7a6864ae31d48d9a6a2f5891e36443c438b53bcf3558c92ec","abstract_canon_sha256":"f2a216a5456f54316aa56abf570df197ad987a24cdd382b6dd5035ecc6e1a66c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:21.238485Z","signature_b64":"yqjW8QLQOCr3mh9lry4RtOQ2+6QjxnWd6LHjv91P/gAEgn8ld4fhW/gQz30UuHy3AfPYFAivu+0LqAedMcneCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3674ee4e8e10284671a80680bf77b3a98de3d54b3a5d1fbccd49a77852e33332","last_reissued_at":"2026-07-05T11:11:21.237977Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:21.237977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homology of Steinberg algebras","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GR","math.OA","math.RA"],"primary_cat":"math.KT","authors_text":"Devarshi Mukherjee, Guido Arnone, Guillermo Corti\\~nas","submitted_at":"2024-12-19T17:54:53Z","abstract_excerpt":"We study homological invariants of the Steinberg algebra $\\mathcal{A}_k(\\mathcal{G})$ of an ample groupoid $\\mathcal{G}$ over a commutative ring $k$. For $\\mathcal{G}$ principal or Hausdorff with ${\\mathcal{G}}^{\\rm{Iso}}\\setminus{\\mathcal{G}}^{(0)}$ discrete, we compute Hochschild and cyclic homology of $\\mathcal{A}_k(\\mathcal{G})$ in terms of groupoid homology. For any ample Hausdorff groupoid $\\mathcal{G}$, we find that $H_*(\\mathcal{G})$ is a direct summand of $HH_*(\\mathcal{A}_k(\\mathcal{G}))$; using this and the Dennis trace we obtain a map $\\overline{D}_*:K_*(\\mathcal{A}_k(\\mathcal{G}))"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15112","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.15112/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.15112","created_at":"2026-07-05T11:11:21.238039+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.15112v4","created_at":"2026-07-05T11:11:21.238039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15112","created_at":"2026-07-05T11:11:21.238039+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZ2O4TUOCAUE","created_at":"2026-07-05T11:11:21.238039+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZ2O4TUOCAUEM4NI","created_at":"2026-07-05T11:11:21.238039+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZ2O4TUO","created_at":"2026-07-05T11:11:21.238039+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21761","citing_title":"Discretisation and independent resolutions of ample groupoids","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG","json":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG.json","graph_json":"https://pith.science/api/pith-number/GZ2O4TUOCAUEM4NIA2AL655TVG/graph.json","events_json":"https://pith.science/api/pith-number/GZ2O4TUOCAUEM4NIA2AL655TVG/events.json","paper":"https://pith.science/paper/GZ2O4TUO"},"agent_actions":{"view_html":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG","download_json":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG.json","view_paper":"https://pith.science/paper/GZ2O4TUO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.15112&json=true","fetch_graph":"https://pith.science/api/pith-number/GZ2O4TUOCAUEM4NIA2AL655TVG/graph.json","fetch_events":"https://pith.science/api/pith-number/GZ2O4TUOCAUEM4NIA2AL655TVG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG/action/storage_attestation","attest_author":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG/action/author_attestation","sign_citation":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG/action/citation_signature","submit_replication":"https://pith.science/pith/GZ2O4TUOCAUEM4NIA2AL655TVG/action/replication_record"}},"created_at":"2026-07-05T11:11:21.238039+00:00","updated_at":"2026-07-05T11:11:21.238039+00:00"}