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Published July 2014 | Submitted + Published
Journal Article Open

Jacobians of noncommutative motives

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 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 J(perf_(dg)(X)) (associated to the derived dg category perf_(dg)(X) of a smooth projective k-scheme X) identifies with the product of all the intermediate algebraic Jacobians of X. As an application, every semi-orthogonal decomposition of the derived category perf(X) gives rise to a decomposition of the intermediate algebraic Jacobians of X.

Additional Information

© 2014 Independent University of Moscow. Received February 07, 2013; in revised form: January 15, 2014. M. Marcolli was supported by the NSF grants DMS-0901221, DMS-1007207, DMS-1201512 and PHY-1205440. G. Tabuada was supported by the NEC Award-2742738 and by the Portuguese Foundation for Science and Technology through the grant PEst-OE/MAT/UI0297/2011 (CMA).

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Published - 2014-014-003-006.pdf

Submitted - 1212.1118v1.pdf

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August 20, 2023
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