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See detailA Riemann-Roch Theorem for dg Algebras
Petit, François UL

in Bulletin de la Société Mathématique de France (2013), 141(2), 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 ... [more ▼]

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. [less ▲]

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