Hochschild cohomology of complex spaces and Noetherian schemes

Abstract

The classical HKR-theorem gives an isomorphism between the n-th Hochschild cohomology of smooth algebras and the n-th exterior power of their module of Kähler differentials. Here, we generalize it for simplicial graded commutative objects in "good pairs of categories". We apply this generalization to complex spaces and Noetherian schemes and deduce several theorems on the decomposition of their respective (relative) Hochschild (co)homologies.