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The formulation of this spectral sequence is similar to the classical case and the calculation of its E_2-term involves the cohomology of certain `brave new Hopf algebroids' E^R_*E. In working out the details we resurrect Adams' original approach to Universal Coefficient Spectral Sequences for modules over an R ring spectrum.\n  We show that the Adams Spectral Sequence for S_R based on a com"},"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":"math/0105079","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2001-05-10T14:18:31Z","cross_cats_sorted":[],"title_canon_sha256":"cf9ea548838582ca8053c35be0cf291ba66321ae2cae05360734cb5206b56462","abstract_canon_sha256":"0f7fd50d4f2611b4d6fb7b88031e5885fe075928fa350e921fed500e5ee66e36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:33.308460Z","signature_b64":"+P3Pus54OQX5LeA95Cy7ySBLgUy8pOI+0O7NZlHFF7CMK6Zjx5vYeIyxmuV8WV6UwGc6bgcokRP3MfTGYHihCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54650c3c2be842e28dbd3efd6e3d51df47baacc98e3dfe31e685adf07a6aa312","last_reissued_at":"2026-05-18T02:41:33.308064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:33.308064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Adams Spectral Sequence for R-modules","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrew Baker, Andrey Lazarev","submitted_at":"2001-05-10T14:18:31Z","abstract_excerpt":"We discuss the Adams Spectral Sequence for R-modules based on commutative localized regular quotient ring spectra over a commutative S-algebra R in the sense of Elmendorf, Kriz, Mandell, May and Strickland. 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