A proper mapping theorem for coadmissible D-modules
We study the behavior of D-modules on rigid analytic varieties under pushforward along a proper morphism. We prove a D-module analogue of Kiehl’s proper mapping theorem, considering the derived sheaf-theoretic pushforward from DX-modules to f∗Dx-modules for proper morphisms f : X → Y . Under assumpt...
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| Format: | Journal article |
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University of Münster
2019
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| _version_ | 1826261214390386688 |
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| author | Bode, A |
| author_facet | Bode, A |
| author_sort | Bode, A |
| collection | OXFORD |
| description | We study the behavior of D-modules on rigid analytic varieties under pushforward along a proper morphism. We prove a D-module analogue of Kiehl’s proper mapping theorem, considering the derived sheaf-theoretic pushforward from DX-modules to f∗Dx-modules for proper morphisms f : X → Y . Under assumptions which can be naturally interpreted as a certain properness condition on the cotangent bundle, we show that any coadmissible Dx-module has coadmissible higher direct images. This implies, among other things, a purely geometric justification of the fact that the global sections functor in the rigid analytic Beilinson–Bernstein correspondence preserves coadmissibility, and we are able to extend this result to twisted DÛ-modules on analytified partial flag varieties |
| first_indexed | 2024-03-06T19:18:00Z |
| format | Journal article |
| id | oxford-uuid:1914ec73-29b7-46a9-a50a-73cf3814314d |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:18:00Z |
| publishDate | 2019 |
| publisher | University of Münster |
| record_format | dspace |
| spelling | oxford-uuid:1914ec73-29b7-46a9-a50a-73cf3814314d2022-03-26T10:46:51ZA proper mapping theorem for coadmissible D-modulesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1914ec73-29b7-46a9-a50a-73cf3814314dSymplectic Elements at OxfordUniversity of Münster2019Bode, AWe study the behavior of D-modules on rigid analytic varieties under pushforward along a proper morphism. We prove a D-module analogue of Kiehl’s proper mapping theorem, considering the derived sheaf-theoretic pushforward from DX-modules to f∗Dx-modules for proper morphisms f : X → Y . Under assumptions which can be naturally interpreted as a certain properness condition on the cotangent bundle, we show that any coadmissible Dx-module has coadmissible higher direct images. This implies, among other things, a purely geometric justification of the fact that the global sections functor in the rigid analytic Beilinson–Bernstein correspondence preserves coadmissibility, and we are able to extend this result to twisted DÛ-modules on analytified partial flag varieties |
| spellingShingle | Bode, A A proper mapping theorem for coadmissible D-modules |
| title | A proper mapping theorem for coadmissible D-modules |
| title_full | A proper mapping theorem for coadmissible D-modules |
| title_fullStr | A proper mapping theorem for coadmissible D-modules |
| title_full_unstemmed | A proper mapping theorem for coadmissible D-modules |
| title_short | A proper mapping theorem for coadmissible D-modules |
| title_sort | proper mapping theorem for coadmissible d modules |
| work_keys_str_mv | AT bodea apropermappingtheoremforcoadmissibledmodules AT bodea propermappingtheoremforcoadmissibledmodules |