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To show this, we (1) make a detailed study of derived completion as a functor $D(A) \\to D(\\widehat{A})$ over a non-noetherian ring $A$; (2) prove a flat base change result for weakly proregular ideals; and (3) Prove that Hochschild cohomology and analytic Hochschild cohomology of complete noetherian local rings"},"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":"1505.04172","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-15T19:28:16Z","cross_cats_sorted":["math.AG","math.KT"],"title_canon_sha256":"bbf936bd18835d4c2e0a6765893cb71e80c0c6cd71ff179486b5b0321767edbc","abstract_canon_sha256":"74d9291cc1fc641859e4c60a264edab361f117597202c4fdd9aca9b0941e7caa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:10.601093Z","signature_b64":"20KkRy9TgPT6YnDiDYXOCXNqUWXLBavpER+STk95V/HBHYbD4cv28SnxQqkrYaMpR0ixuvVshcYiWbYr6i/wAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f9468bc84bc9827465ad4706473b507d27fb017e2c51133aeec5e68cb61692f","last_reissued_at":"2026-05-18T01:10:10.600473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:10.600473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hochschild cohomology commutes with adic completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.AC","authors_text":"Liran Shaul","submitted_at":"2015-05-15T19:28:16Z","abstract_excerpt":"For a flat commutative $k$-algebra $A$ such that the enveloping algebra $A\\otimes_k A$ is noetherian, given a finitely generated bimodule $M$, we show that the adic completion of the Hochschild cohomology module $HH^n(A/k,M)$ is naturally isomorphic to $HH^n(\\widehat{A}/k,\\widehat{M})$. 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