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For $X$ smooth and projective, we show that this spectral sequence degenerates, leading to an explicit relation between the equivariant and the ordinary higher Chow groups. We obtain several applications to algebraic $K$-theory.\n  We show that for a reductive group $G$ acting on a smooth projective scheme $X$, the forgetful map $K^G_i(X) \\to K_i(X)$ induces an isomorphism $K^G_i(X)/{I_G K^G_i(X)} \\"},"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":"0906.3109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-17T08:42:18Z","cross_cats_sorted":[],"title_canon_sha256":"27a38f6989e09ee9f1633f1169461fe39f79140b595a71887845c2dd7a682c88","abstract_canon_sha256":"a7781891f005d28bc63b4b0e81a0cf970ba5392b3052329d152b906bd9694657"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:12.821484Z","signature_b64":"ke97vNJ1njmuRVJ+5HFJFCQ+7enc8wFeG+ZskPS+EqGjXghgqfS+zUNacPBasa0Sp38nqA7RcbMUhxnjaCUPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"788cb9f8ed1b3329d62f862f610baf462ea02013dc6b9dd68753831f12eedc26","last_reissued_at":"2026-05-18T00:56:12.820826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:12.820826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant K-theory and Higher Chow Groups of Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amalendu Krishna","submitted_at":"2009-06-17T08:42:18Z","abstract_excerpt":"For a smooth quasi-projective scheme $X$ over a field $k$ with an action of a reductive group, we establish a spectral sequence connecting the equivariant and the ordinary higher Chow groups of $X$. 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