Algebraic Geometry
A generalized Hirzebruch Riemann–Roch theorem

Presented by: Christophe Soulé

Ramadoss, Ajay C.1
1 Department of Mathematics, Cornell University, 580 Malott Hall, Ithaca, NY 14853, USA
Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 289-292.

This short Note proves a generalization of the Hirzebruch Riemann–Roch theorem equivalent to the Cardy condition. This is done using an earlier result that explicitly describes what the Mukai pairing on Hochschild homology descends to in Hodge cohomology via the Hochschild–Kostant–Rosenberg map twisted by the root Todd genus.

Nous montrons dans cette Note une généralisation du théorème de Hirzebruch–Riemann–Roch, équivalente à la condition de Cardy. On s'appuie pour cela sur un résultat antérieur décrivant l'accouplement de Mukai sur la cohomologie de Hochschild en termes de la cohomologie de Hodge, via l'application de Hochschild–Kostant–Rosenberg tordue par le genre de Todd de la base.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.01.015
Ramadoss, Ajay C. 1

1 Department of Mathematics, Cornell University, 580 Malott Hall, Ithaca, NY 14853, USA 
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Ramadoss, Ajay C. A generalized Hirzebruch Riemann–Roch theorem. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 289-292. doi : 10.1016/j.crma.2009.01.015. http://www.numdam.org/articles/10.1016/j.crma.2009.01.015/

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[3] Ishikawa, H.; Tani, T. Twisted boundary states and representation of generalized fusion algebra (preprint) | arXiv

[4] N. Markarian, Poincare–Brikhoff–Witt isomorphism, Hochschild homology and the Riemann–Roch theorem, MPI preprint MPI 2001-52

[5] Ramadoss, A. The relative Riemann–Roch theorem from Hochschild homology, New York Journal of Mathematics, Volume 14 (2008), pp. 643-717

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