Jacobians of Noncommutative Motives
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...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Independent University of Moscow
2015
|
| Online Access: | http://hdl.handle.net/1721.1/93242 https://orcid.org/0000-0001-5558-9236 |
| _version_ | 1811095028133527552 |
|---|---|
| author | Trigo Neri Tabuada, Goncalo Jo Marcolli, Matilde |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jo Marcolli, Matilde |
| author_sort | Trigo Neri Tabuada, Goncalo Jo |
| collection | MIT |
| description | 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[subscript dg](X)) (associated to the derived dg category perf[subscript 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. |
| first_indexed | 2024-09-23T16:09:21Z |
| format | Article |
| id | mit-1721.1/93242 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:09:21Z |
| publishDate | 2015 |
| publisher | Independent University of Moscow |
| record_format | dspace |
| spelling | mit-1721.1/932422022-10-02T06:41:43Z Jacobians of Noncommutative Motives Trigo Neri Tabuada, Goncalo Jo Marcolli, Matilde Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jo 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[subscript dg](X)) (associated to the derived dg category perf[subscript 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. NEC Corporation (Award 2742738) Portuguese Science and Technology Foundation (PEst-OE/MAT/UI0297/2011) 2015-01-30T19:40:22Z 2015-01-30T19:40:22Z 2014-07 2014-01 Article http://purl.org/eprint/type/JournalArticle 1609-4514 1609-3321 http://hdl.handle.net/1721.1/93242 Marcolli, Matilde, and Goncalo Tabuada. "Jacobians of Noncommutative Motives." Moscow Mathematical Journal, Volume 14, Number 3 (July-September 2014), 577-594. https://orcid.org/0000-0001-5558-9236 en_US http://www.mathjournals.org/mmj/2014-014-003/2014-014-003-006.pdf Moscow Mathematical Journal Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Independent University of Moscow arXiv |
| spellingShingle | Trigo Neri Tabuada, Goncalo Jo Marcolli, Matilde Jacobians of Noncommutative Motives |
| title | Jacobians of Noncommutative Motives |
| title_full | Jacobians of Noncommutative Motives |
| title_fullStr | Jacobians of Noncommutative Motives |
| title_full_unstemmed | Jacobians of Noncommutative Motives |
| title_short | Jacobians of Noncommutative Motives |
| title_sort | jacobians of noncommutative motives |
| url | http://hdl.handle.net/1721.1/93242 https://orcid.org/0000-0001-5558-9236 |
| work_keys_str_mv | AT trigoneritabuadagoncalojo jacobiansofnoncommutativemotives AT marcollimatilde jacobiansofnoncommutativemotives |