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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A sheaf of Hochschild complexes on quasi-compact opens
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by Wendy Lowen PDF
Proc. Amer. Math. Soc. 136 (2008), 3045-3050 Request permission

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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Additional Information
  • Wendy Lowen
  • Affiliation: Departement DWIS, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
  • Email: wlowen@vub.ac.be
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3045-3050
  • MSC (2000): Primary 18E15, 18F20
  • DOI: https://doi.org/10.1090/S0002-9939-08-09471-9
  • MathSciNet review: 2407066