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A sheaf of Hochschild complexes on quasi-compact opens

Author: Wendy Lowen
Journal: Proc. Amer. Math. Soc. 136 (2008), 3045-3050
MSC (2000): Primary 18E15, 18F20
Published electronically: April 17, 2008
MathSciNet review: 2407066
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Abstract: For a scheme $ X$, we construct a sheaf $ \mathbf{C}$ of complexes on $ X$ such that for every quasi-compact open $ U \subset X$, $ \mathbf{C}(U)$ is quasi-isomorphic to the Hochschild complex of $ U$ (Lowen and Van den Bergh, 2005). Since $ \mathbf{C}$ is moreover acyclic for taking sections on quasi-compact opens, we obtain a local to global spectral sequence for Hochschild cohomology if $ X$ is quasi-compact.

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Wendy Lowen
Affiliation: Departement DWIS, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium

Received by editor(s): September 18, 2006
Received by editor(s) in revised form: June 25, 2007, and July 10, 2007
Published electronically: April 17, 2008
Additional Notes: The author is a Postdoctoral fellow FWO/CNRS. She acknowledges the hospitality of the Institut de Mathématiques de Jussieu (IMJ) and of the Institut des Hautes Études Scientifiques (IHES) during her postdoctoral fellowship with CNRS
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.