### Abstract

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 J(N) agrees with the subspace of the odd periodic cyclic homology of N which is generated by algebraic curves; (ii) the abelian variety J(perf(X)) (associated to the derived dg category perf(X) of a smooth projective scheme X) identifies with the union of all the intermediate algebraic Jacobians of X.

Original language | Unknown |
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Pages (from-to) | 577-594 |

Journal | Moscow Mathematical Journal |

Volume | 14 |

Issue number | 3 |

Publication status | Published - 1 Jan 2014 |

## Cite this

Tabuada, G. J. T. N. (2014). Jacobians of noncommutative motives.

*Moscow Mathematical Journal*,*14*(3), 577-594.