Homology, Homotopy and Applications
- Homology Homotopy Appl.
- Volume 6, Number 1 (2004), 299-340.
Hochschild cohomology of complex spaces and Noetherian schemes
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.
Homology Homotopy Appl., Volume 6, Number 1 (2004), 299-340.
First available in Project Euclid: 13 February 2006
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
Secondary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Schuhmacher, Frank. Hochschild cohomology of complex spaces and Noetherian schemes. Homology Homotopy Appl. 6 (2004), no. 1, 299--340. https://projecteuclid.org/euclid.hha/1139839556