{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DZKF2RRYU73E5XY2IQRY2UXV2W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8a160e234d6a4d8c55f4af43cac49f43b1105c0ce88b9a53f92e501739542bf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-02T09:39:30Z","title_canon_sha256":"e3642483418275ae182cd981d67ce9b19f1d2ef14dd63839950cf2152bb7bbd1"},"schema_version":"1.0","source":{"id":"1009.0363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0363","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0363v1","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0363","created_at":"2026-05-18T04:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"DZKF2RRYU73E","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DZKF2RRYU73E5XY2","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DZKF2RRY","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:1a3fb0f11f56e5e6c6591db5be5daca9e0bf7101ae3cc2c1ddd8f12164fb950e","target":"graph","created_at":"2026-05-18T04:41:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For certain tame abelian covers of arithmetic surfaces X/Y we obtain striking formulas, involving a quadratic form derived from intersection numbers, for the equivariant Euler characteristics of both the canonical sheaf !X/Y and also its square root !1/2 X/Y . These formulas allow us us to carry out explicit calculations; in particular, we are able to exhibit examples where these two Euler characteristics and that of the the structure sheaf of X are all different and non-trivial. Our results are obtained by using resolvent techniques together with the local Riemann-Roch approach developed in [","authors_text":"M.J. Taylor, Ph. Cassou-Nogu`es","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-02T09:39:30Z","title":"Equivariant Euler characteristics and sheaf resolvents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0363","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:94ee27433a1597576dad342480f159046da4407b87e4b59b25b80ff6f305c7ab","target":"record","created_at":"2026-05-18T04:41:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8a160e234d6a4d8c55f4af43cac49f43b1105c0ce88b9a53f92e501739542bf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-02T09:39:30Z","title_canon_sha256":"e3642483418275ae182cd981d67ce9b19f1d2ef14dd63839950cf2152bb7bbd1"},"schema_version":"1.0","source":{"id":"1009.0363","kind":"arxiv","version":1}},"canonical_sha256":"1e545d4638a7f64edf1a44238d52f5d59a5191b5968647e2aab5486296142c05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e545d4638a7f64edf1a44238d52f5d59a5191b5968647e2aab5486296142c05","first_computed_at":"2026-05-18T04:41:26.865960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:26.865960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s+hhFpiUKWDpu73EFnr4rpyD0XayE6NvJzxdq1ARuOBKXjWgSegoSisDgKElymbAeyHwsFG1GBLdh4PjKsUNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:26.866665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94ee27433a1597576dad342480f159046da4407b87e4b59b25b80ff6f305c7ab","sha256:1a3fb0f11f56e5e6c6591db5be5daca9e0bf7101ae3cc2c1ddd8f12164fb950e"],"state_sha256":"a6d4b4f90d0a4fe0e8c2bb5e9228be187d5322eec51d86f068656c6b5408c738"}