Equivariant gerbes on complex tori
We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line bundles. The theta group of symmetries of the gerbe has the stru...
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1797075559183810560 |
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| author | Ben-Bassat, O |
| author_facet | Ben-Bassat, O |
| author_sort | Ben-Bassat, O |
| collection | OXFORD |
| description | We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line bundles. The theta group of symmetries of the gerbe has the structure of a Picard groupoid. We calculate it explicitly as a central extension of the group of symmetries of the gerbe by the Picard groupoid of the underlying complex torus. We discuss obstruction to equivariance and give an example of a group of symmetries of a gerbe with respect to which the gerbe cannot be equivariant. We calculate the obstructions to invariant gerbes for some group of translations of a torus to be equivariant. We survey various types of representations of the group of symmetries of a gerbe on the stack of sheaves of modules on the gerbe and the associated abelian category of sheaves on the gerbe (twisted sheaves). © 2012 Elsevier B.V. |
| first_indexed | 2024-03-06T23:52:01Z |
| format | Journal article |
| id | oxford-uuid:72ec999d-d50f-416c-a982-4683532dede9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:52:01Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:72ec999d-d50f-416c-a982-4683532dede92022-03-26T19:53:12ZEquivariant gerbes on complex toriJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:72ec999d-d50f-416c-a982-4683532dede9EnglishSymplectic Elements at Oxford2013Ben-Bassat, OWe explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line bundles. The theta group of symmetries of the gerbe has the structure of a Picard groupoid. We calculate it explicitly as a central extension of the group of symmetries of the gerbe by the Picard groupoid of the underlying complex torus. We discuss obstruction to equivariance and give an example of a group of symmetries of a gerbe with respect to which the gerbe cannot be equivariant. We calculate the obstructions to invariant gerbes for some group of translations of a torus to be equivariant. We survey various types of representations of the group of symmetries of a gerbe on the stack of sheaves of modules on the gerbe and the associated abelian category of sheaves on the gerbe (twisted sheaves). © 2012 Elsevier B.V. |
| spellingShingle | Ben-Bassat, O Equivariant gerbes on complex tori |
| title | Equivariant gerbes on complex tori |
| title_full | Equivariant gerbes on complex tori |
| title_fullStr | Equivariant gerbes on complex tori |
| title_full_unstemmed | Equivariant gerbes on complex tori |
| title_short | Equivariant gerbes on complex tori |
| title_sort | equivariant gerbes on complex tori |
| work_keys_str_mv | AT benbassato equivariantgerbesoncomplextori |