Moscow Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mosc. Math. J., 2014, Volume 14, Number 3, Pages 577–594 (Mi mmj533)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.17323/1609-4514-2014-14-3-577-594

Full text: http://www.mathjournals.org/.../2014-014-003-006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14C15, 14H40, 14K02, 14K30, 18D20
Received: February 7, 2013; in revised form January 15, 2014
Language:

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://www.ams.org/mathscinet-getitem?mr=3241760}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789400006}


Linking options:
  • http://mi.mathnet.ru/eng/mmj533
  • http://mi.mathnet.ru/eng/mmj/v14/i3/p577

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Bernardara, G. Tabuada, “Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives”, Izv. Math., 80:3 (2016), 463–480  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Marcello Bernardara, Gonçalo Tabuada, “From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives”, Mosc. Math. J., 16:2 (2016), 205–235  mathnet  crossref  mathscinet
    3. A. Blanc, “Topological $K$-theory of complex noncommutative spaces”, Compos. Math., 152:3 (2016), 489–555  crossref  mathscinet  zmath  isi  scopus
    4. J. Calabrese, “A note on derived equivalences and birational geometry”, Bull. London Math. Soc., 49:3 (2017), 499–504  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
    Number of views:
    This page:105
    References:26

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021