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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 863-866 (août 2008)
Doi : 10.1016/j.crma.2008.05.017
Received : 21 Mars 2008 ;  accepted : 26 May 2008
The module structure of Hochschild homology in some examples
La structure module de lʼhomologie de Hochschild dans quelques exemples
 

Emanuele Macri` a , Marc Nieper-Wißkirchen b , Paolo Stellari c
a Hausdorff Center for Mathematics, Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany 
b Institut für Mathematik, Johannes-Gutenberg-Universität, Staudinger Weg 9, 55128 Mainz, Germany 
c Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy 

Abstract

In this Note we give a simple proof of a conjecture by A. Căldăraru stating the compatibility between the modified Hochschild–Kostant–Rosenberg isomorphism and the action of Hochschild cohomology on Hochschild homology in the case of Calabi–Yau manifolds and smooth projective curves. To cite this article: E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

Dans cette Note nous donnons une démonstration simple dʼune conjecture dʼA. Căldăraru énoncant la compatibilité entre lʼisomorphisme modifié de Hochschild–Kostant–Rosenberg et lʼaction de la cohomologie de Hochschild sur lʼhomologie de Hochschild dans le cas des variétés de Calabi–Yau et des courbes projectives régulières. Pour citer cet article : E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

 This work was supported by the SFB/TR 45 “Periods, Moduli Spaces and Arithmetic of Algebraic Varieties” of the DFG (German Research Foundation).



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