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For any functor $F:{D}(A)\\times\\dots\\times{D}(A)\\to{D}(B)$ between their derived categories, we define its twist $F^{!}:{D}(A)\\times\\dots\\times{D}(A)\\to{D}(B)$ with respect to dualizing complexes, generalizing Grothendieck's construction of $f^{!}$. We show that relations between functors are preserved between their twists, and deduce that various relations hold between derived Hochschild (co)-homology and the $f^{!}$ functor. We also deduce that the set of isomorphism classes of dualizing complexes over a ring ("},"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":"1401.6678","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-01-26T18:44:03Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"660cdd2fd4207b28960501d230d91f023ce189dedf1e035943278ee67df589f1","abstract_canon_sha256":"63a4318329b901a18f3007e8ebebc2c86c1f31930008aaead2c7850140c57da9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:27.661993Z","signature_b64":"17AjoGcsgb61T5tdG9r3ZKxdbxpZyddFWV9l32pypbOCRCTNEOqNwyqtGt2UexnJRko09T8wBmga3E+FhY0DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9e6e68f19d5f298ad0977089cb7baae2566161394b5831e9010d1adeb893538","last_reissued_at":"2026-05-18T01:11:27.661440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:27.661440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relations between derived Hochschild functors via twisting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Liran Shaul","submitted_at":"2014-01-26T18:44:03Z","abstract_excerpt":"Let $k$ be a regular ring, and let $A,B$ be essentially finite type $k$-algebras. For any functor $F:{D}(A)\\times\\dots\\times{D}(A)\\to{D}(B)$ between their derived categories, we define its twist $F^{!}:{D}(A)\\times\\dots\\times{D}(A)\\to{D}(B)$ with respect to dualizing complexes, generalizing Grothendieck's construction of $f^{!}$. We show that relations between functors are preserved between their twists, and deduce that various relations hold between derived Hochschild (co)-homology and the $f^{!}$ functor. 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