Homology, Homotopy and Applications
Volume 6 (2004)
Hochschild cohomology of complex spaces and Noetherian schemes
Pages: 299 – 340
The classical HKR-theorem gives an isomorphism between the n-th Hochschild cohomology of smooth algebras and the nth 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.
admissible pair of categories, complex space, Hochschild cohomology, regular sequence, scheme
2010 Mathematics Subject Classification