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In this paper we prove a formula (Theorem 8.1, the residue formula) for the evaluation on the fundamental class of $\\xred$ of any $\\eta_0 \\in H^*(\\xred)$ whose degree is the dimension of $\\xred$, provided that $0$ is a regular value "},"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":"alg-geom/9307001","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-07-06T22:55:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6a25c95af456780d57a2cd82426ade17547a9755723e8aabc0720e60fe573a34","abstract_canon_sha256":"d80d9fcd0fe90a2bc45d0bcd32e3c98f0dab696e9a12a2cbd8bba43d0e6acde5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:07:12.829564Z","signature_b64":"TlUw6HgHfuriJjrCO8BezI5BSxImdhYBF0PiMrC5Br9oZqsBCyppMMDuiaqmDY6EV8rX+QnM/TOxa7yP8V4mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39af074ba6d4dac3f120582a5458cbd663f17d4aa81b4bf4db236b7163a5fdb8","last_reissued_at":"2026-07-04T15:07:12.829167Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:07:12.829167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Localization for nonabelian group actions","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"F.C. 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