Relations between derived Hochschild functors via twisting

Abstract

Let $k$ be a regular ring, and let $A,B$ be essentially finite type $k$-algebras. For any functor $F:D(A)\times \cdots \times D(A)\to D(B)$ between their derived categories, we define its twist $F^{!}:D(A)\times \cdots \times D(A)\to D(B)$ 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 (or a scheme) form a group with respect to derived Hochschild cohomology, and that the twisted inverse image functor is a group homomorphism.

8 pages, final version, to appear in Comm. Algebra

Cited by in corpus (2)

• Derived Categories
• The twisted inverse image pseudofunctor over commutative DG rings and perfect base change