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 Jacobians of noncommutative motives

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In this article one extends the classical theory of intermediate Jacobians to the -noncommutative world-. Concretely, one constructs a Q-linear additive Jacobian functor J- from the category of noncommutative Chow motives to the category of abelian varieties up to isogeny, with the following properties: i the first de Rham cohomology group of JN agrees with the subspace of the odd periodic cyclic homology of N which is generated by algebraic curves; ii the abelian variety JperfX associated to the derived dg category perfX of a smooth projective scheme X identifies with the union of all the intermediate algebraic Jacobians of X.

Author: Matilde Marcolli; Goncalo Tabuada

Source: https://archive.org/

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