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Jacobians of Noncommutative Motives
Moscow Mathematical Journal
In this article one extends the classical theory of (intermediate) Jacobians to the "noncommutative world". Concretely, one constructs a Q-linear additive Jacobian functor N → J (N ) 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 Jdoi:10.17323/1609-4514-2014-14-3-577-594 fatcat:omh2xgh5cnat3poaokla4fliwm