The de Rham functor for logarithmic D-modules
In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain...
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| Format: | Journal article |
| Language: | English |
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Springer Verlag
2020
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| _version_ | 1826269603549937664 |
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| author | Koppensteiner, C |
| author_facet | Koppensteiner, C |
| author_sort | Koppensteiner, C |
| collection | OXFORD |
| description | In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain graded sheaves on the so-called Kato–Nakayama space. For holonomic modules we show that the associated sheaves have finitely generated stalks and that the de Rham functor intertwines duality for D-modules with a version of Poincaré–Verdier duality on the Kato–Nakayama space. Finally, we explain how the grading on the Kato–Nakayama space is related to the classical Kashiwara–Malgrange V-filtration for holonomic D-modules. |
| first_indexed | 2024-03-06T21:27:39Z |
| format | Journal article |
| id | oxford-uuid:43a169e8-3eda-4f19-b3de-4a5cc236ce0a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:27:39Z |
| publishDate | 2020 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:43a169e8-3eda-4f19-b3de-4a5cc236ce0a2022-03-26T14:56:37ZThe de Rham functor for logarithmic D-modulesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:43a169e8-3eda-4f19-b3de-4a5cc236ce0aEnglishSymplectic ElementsSpringer Verlag2020Koppensteiner, CIn the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain graded sheaves on the so-called Kato–Nakayama space. For holonomic modules we show that the associated sheaves have finitely generated stalks and that the de Rham functor intertwines duality for D-modules with a version of Poincaré–Verdier duality on the Kato–Nakayama space. Finally, we explain how the grading on the Kato–Nakayama space is related to the classical Kashiwara–Malgrange V-filtration for holonomic D-modules. |
| spellingShingle | Koppensteiner, C The de Rham functor for logarithmic D-modules |
| title | The de Rham functor for logarithmic D-modules |
| title_full | The de Rham functor for logarithmic D-modules |
| title_fullStr | The de Rham functor for logarithmic D-modules |
| title_full_unstemmed | The de Rham functor for logarithmic D-modules |
| title_short | The de Rham functor for logarithmic D-modules |
| title_sort | de rham functor for logarithmic d modules |
| work_keys_str_mv | AT koppensteinerc thederhamfunctorforlogarithmicdmodules AT koppensteinerc derhamfunctorforlogarithmicdmodules |