Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

Hochschild cohomology of complex spaces and Noetherian schemes

Pages: 299 – 340

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a17


Frank Schuhmacher (Institut Fourier, UMR 5582, Saint Martin d’Hères, France)


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

13D03, 14F43

Full Text (PDF format)