Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories
To every scheme, not necessarily smooth neither proper, we can associate its different mixed realizations (de Rham, Betti, étale, Hodge, etc.) as well as its ring of periods. In this note, following an insight of Kontsevich, we prove that, after suitable modifications, these classical constructions...
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Oxford University Press (OUP)
2018
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| Online dostop: | http://hdl.handle.net/1721.1/116052 https://orcid.org/0000-0001-5558-9236 |
| _version_ | 1826199221605236736 |
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| author | Trigo Neri Tabuada, Goncalo Jorge |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge |
| author_sort | Trigo Neri Tabuada, Goncalo Jorge |
| collection | MIT |
| description | To every scheme, not necessarily smooth neither proper, we can associate its different mixed realizations (de Rham, Betti, étale, Hodge, etc.) as well as its ring of periods. In this note, following an insight of Kontsevich, we prove that, after suitable modifications, these classical constructions can be extended from schemes to the broad setting of differential graded (dg) categories. This leads to new additive invariants of dg categories, which we compute in the case of differential operators, as well as to a theory of periods of dg categories. Among other applications, we prove that the ring of periods of a scheme is invariant under projective homological duality. Along the way, we explicitly describe the modified mixed realizations using the Tannakian formalism. |
| first_indexed | 2024-09-23T11:16:40Z |
| format | Article |
| id | mit-1721.1/116052 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:16:40Z |
| publishDate | 2018 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1160522022-09-27T18:22:50Z Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories Trigo Neri Tabuada, Goncalo Jorge Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge To every scheme, not necessarily smooth neither proper, we can associate its different mixed realizations (de Rham, Betti, étale, Hodge, etc.) as well as its ring of periods. In this note, following an insight of Kontsevich, we prove that, after suitable modifications, these classical constructions can be extended from schemes to the broad setting of differential graded (dg) categories. This leads to new additive invariants of dg categories, which we compute in the case of differential operators, as well as to a theory of periods of dg categories. Among other applications, we prove that the ring of periods of a scheme is invariant under projective homological duality. Along the way, we explicitly describe the modified mixed realizations using the Tannakian formalism. 2018-06-04T15:11:06Z 2018-06-04T15:11:06Z 2016-11 2016-08 2018-05-31T16:24:38Z Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 http://hdl.handle.net/1721.1/116052 Tabuada, Gonçalo. “Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories.” International Mathematics Research Notices (December 2016): rnw242 https://orcid.org/0000-0001-5558-9236 http://dx.doi.org/10.1093/IMRN/RNW242 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Trigo Neri Tabuada, Goncalo Jorge Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories |
| title | Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories |
| title_full | Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories |
| title_fullStr | Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories |
| title_full_unstemmed | Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories |
| title_short | Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories |
| title_sort | modified mixed realizations new additive invariants and periods of dg categories |
| url | http://hdl.handle.net/1721.1/116052 https://orcid.org/0000-0001-5558-9236 |
| work_keys_str_mv | AT trigoneritabuadagoncalojorge modifiedmixedrealizationsnewadditiveinvariantsandperiodsofdgcategories |