  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.
