Jacobians of noncommutative motives

Matilde Marcolli; Goncalo Tabuada

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arXiv · 1212.1118

Jacobians of noncommutative motives

Matilde Marcolli·Goncalo Tabuada

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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.

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BibTeX RIS

Matilde Marcolli, Goncalo Tabuada. 2012-12-05. Jacobians of noncommutative motives. https://arxiv.org/abs/1212.1118

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