Relations Between Derived Hochschild Functors via Twisting

Liran Shaul

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let (Figure presented.) be a regular ring, and let A, B be essentially finite type (Figure presented.) -algebras. For any functor F: D(ModA) × ⋅ × D(ModA) → D(ModB) between their derived categories, we define its twist F!: D(ModA) × ⋅ × D(ModA) → D(ModB) 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 (or a scheme) form a group with respect to derived Hochschild cohomology, and that the twisted inverse image functor is a group homomorphism.

Original languageEnglish
Pages (from-to)2898-2907
Number of pages10
JournalCommunications in Algebra
Issue number7
StatePublished - 2 Jul 2016
Externally publishedYes


  • Dualizing complex
  • Hochschild cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory


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