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Moscow Mathematical Journal, 2014, Volume 14, Number 3, Pages 577–594
DOI: https://doi.org/10.17323/1609-4514-2014-14-3-577-594
(Mi mmj533)
 

This article is cited in 5 scientific papers (total in 5 papers)

Jacobians of noncommutative motives

Matilde Marcollia, Gonçalo Tabuadabc

a Mathematics Department, Mail Code 253-37, Caltech, 1200 E. California Blvd. Pasadena, CA 91125, USA
b Departamento de Matemática e CMA, FCT-UNL, Quinta da Torre, 2829-516 Caparica, Portugal
c Department of Mathematics, MIT, Cambridge, MA 02139, USA
Full-text PDF Citations (5)
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Abstract: In this article one extends the classical theory of (intermediate) Jacobians to the “noncommutative world”. Concretely, one constructs a $\mathbb Q$-linear additive Jacobian functor $N\mapsto\boldsymbol J(N)$ 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 $\boldsymbol J(N)$ agrees with the subspace of the odd periodic cyclic homology of $N$ which is generated by algebraic curves; (ii) the abelian variety $\boldsymbol J(\mathrm{perf}_\mathrm{dg}(X))$ (associated to the derived dg category $\mathrm{perf}_\mathrm{dg}(X)$ 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 $\mathrm{perf}(X)$ gives rise to a decomposition of the intermediate algebraic Jacobians of $X$.
Key words and phrases: Jacobians, abelian varieties, isogeny, noncommutative motives.
Received: February 7, 2013; in revised form January 15, 2014
Bibliographic databases:
Document Type: Article
Language: English
Citation: Matilde Marcolli, Gonçalo Tabuada, “Jacobians of noncommutative motives”, Mosc. Math. J., 14:3 (2014), 577–594
Citation in format AMSBIB
\Bibitem{MarTab14}
\by Matilde~Marcolli, Gon{\c c}alo~Tabuada
\paper Jacobians of noncommutative motives
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 3
\pages 577--594
\mathnet{http://mi.mathnet.ru/mmj533}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-3-577-594}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241760}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000342789400006}
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  • This publication is cited in the following 5 articles:
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