D-modules on rigid analytic spaces
We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small affinoid varieties are Fréchet-Stein algebras, and use this to define co-admi...
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| Format: | Journal article |
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De Gruyter
2016
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| _version_ | 1797085499403272192 |
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| author | Ardakov, K Wadsley, S |
| author_facet | Ardakov, K Wadsley, S |
| author_sort | Ardakov, K |
| collection | OXFORD |
| description | We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small affinoid varieties are Fréchet-Stein algebras, and use this to define co-admissible sheaves of D-modules. We prove analogues of Cartan’s Theorems A and B for co-admissible D-modules. |
| first_indexed | 2024-03-07T02:09:43Z |
| format | Journal article |
| id | oxford-uuid:a0342caf-2b1d-4f7d-9a4c-73a7774b1f26 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:09:43Z |
| publishDate | 2016 |
| publisher | De Gruyter |
| record_format | dspace |
| spelling | oxford-uuid:a0342caf-2b1d-4f7d-9a4c-73a7774b1f262022-03-27T02:03:43ZD-modules on rigid analytic spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a0342caf-2b1d-4f7d-9a4c-73a7774b1f26Symplectic Elements at OxfordDe Gruyter2016Ardakov, KWadsley, SWe introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small affinoid varieties are Fréchet-Stein algebras, and use this to define co-admissible sheaves of D-modules. We prove analogues of Cartan’s Theorems A and B for co-admissible D-modules. |
| spellingShingle | Ardakov, K Wadsley, S D-modules on rigid analytic spaces |
| title | D-modules on rigid analytic spaces |
| title_full | D-modules on rigid analytic spaces |
| title_fullStr | D-modules on rigid analytic spaces |
| title_full_unstemmed | D-modules on rigid analytic spaces |
| title_short | D-modules on rigid analytic spaces |
| title_sort | d modules on rigid analytic spaces |
| work_keys_str_mv | AT ardakovk dmodulesonrigidanalyticspaces AT wadsleys dmodulesonrigidanalyticspaces |