Non-commutative tori and Fourier-Mukai duality
The classical Fourier-Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects. Both of these are generalized deformations of the complex tor...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797089724338274304 |
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| author | Ben-Bassat, O Block, J Pantev, T |
| author_facet | Ben-Bassat, O Block, J Pantev, T |
| author_sort | Ben-Bassat, O |
| collection | OXFORD |
| description | The classical Fourier-Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects. Both of these are generalized deformations of the complex tori. In one case, a complex torus is deformed formally in a non-commutative direction specified by a holomorphic Poisson structure. In the other, the dual complex, torus is deformed in a B-field direction to a formal gerbe. We show that these two deformations are Fourier-Mukai equivalent. © Foundation Compositio Mathematica 2007. |
| first_indexed | 2024-03-07T03:08:11Z |
| format | Journal article |
| id | oxford-uuid:b3476a7e-5528-49bd-8936-8aef3b03f9a6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:08:11Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:b3476a7e-5528-49bd-8936-8aef3b03f9a62022-03-27T04:17:49ZNon-commutative tori and Fourier-Mukai dualityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b3476a7e-5528-49bd-8936-8aef3b03f9a6EnglishSymplectic Elements at Oxford2007Ben-Bassat, OBlock, JPantev, TThe classical Fourier-Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects. Both of these are generalized deformations of the complex tori. In one case, a complex torus is deformed formally in a non-commutative direction specified by a holomorphic Poisson structure. In the other, the dual complex, torus is deformed in a B-field direction to a formal gerbe. We show that these two deformations are Fourier-Mukai equivalent. © Foundation Compositio Mathematica 2007. |
| spellingShingle | Ben-Bassat, O Block, J Pantev, T Non-commutative tori and Fourier-Mukai duality |
| title | Non-commutative tori and Fourier-Mukai duality |
| title_full | Non-commutative tori and Fourier-Mukai duality |
| title_fullStr | Non-commutative tori and Fourier-Mukai duality |
| title_full_unstemmed | Non-commutative tori and Fourier-Mukai duality |
| title_short | Non-commutative tori and Fourier-Mukai duality |
| title_sort | non commutative tori and fourier mukai duality |
| work_keys_str_mv | AT benbassato noncommutativetoriandfouriermukaiduality AT blockj noncommutativetoriandfouriermukaiduality AT pantevt noncommutativetoriandfouriermukaiduality |