Homology, Homotopy and Applications

Hochschild cohomology of complex spaces and Noetherian schemes

Frank Schuhmacher

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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.

Article information

Source
Homology Homotopy Appl., Volume 6, Number 1 (2004), 299-340.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139839556

Mathematical Reviews number (MathSciNet)
MR2084590

Zentralblatt MATH identifier
1070.18010

Subjects
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)

Citation

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


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