A Riemann-Roch theorem for dg algebras
Bulletin de la Société Mathématique de France, Volume 141 (2013) no. 2, p. 197-223

Given a smooth proper dg algebra A, a perfect dg A-module M and an endomorphism f of M, we define the Hochschild class of the pair (M,f) with values in the Hochschild homology of the algebra A. Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.

Étant donnée une dg algèbre A, propre et lisse, un dg A-module parfait M et un endomorphisme f de M, nous définissons la classe de Hochschild de la paire (M,f). Cette classe est à valeurs dans l’homologie de Hochschild de l’algèbre A. Notre principal résultat est une formule de type Riemann-Roch faisant intervenir la convolution de deux de ces classes de Hochschild.

DOI : https://doi.org/10.24033/bsmf.2646
Classification:  14C40,  16E40,  16E45
Keywords: differential graded algebra, perfect module, Serre duality, Hochschild homology, Hochschild class, Riemann-Roch theorem
@article{BSMF_2013__141_2_197_0,
     author = {Petit, Fran\c cois},
     title = {A Riemann-Roch theorem for dg algebras},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {141},
     number = {2},
     year = {2013},
     pages = {197-223},
     doi = {10.24033/bsmf.2646},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2013__141_2_197_0}
}
Petit, François. A Riemann-Roch theorem for dg algebras. Bulletin de la Société Mathématique de France, Volume 141 (2013) no. 2, pp. 197-223. doi : 10.24033/bsmf.2646. http://www.numdam.org/item/BSMF_2013__141_2_197_0/

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