The analytic de Rham stack in rigid geometry
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909073508663296 |
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| author | Camargo, Juan Esteban Rodríguez |
| author_facet | Camargo, Juan Esteban Rodríguez |
| contents | Applying the new theory of analytic stacks of Clausen and Scholze we introduce a general notion of derived Tate adic spaces. We use this formalism to define the analytic de Rham stack in rigid geometry, extending the theory of $D$-cap-modules of Ardakov and Wadsley to the theory of analytic $D$-modules. We prove some foundational results such as the existence of a six functor formalism and Poincaré duality for analytic $D$-modules, generalizing previous work of Bode. Finally, we relate the theory of analytic $D$-modules to previous work of the author with Rodrigues Jacinto on solid locally analytic representations of $p$-adic Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The analytic de Rham stack in rigid geometry Camargo, Juan Esteban Rodríguez Algebraic Geometry Representation Theory Applying the new theory of analytic stacks of Clausen and Scholze we introduce a general notion of derived Tate adic spaces. We use this formalism to define the analytic de Rham stack in rigid geometry, extending the theory of $D$-cap-modules of Ardakov and Wadsley to the theory of analytic $D$-modules. We prove some foundational results such as the existence of a six functor formalism and Poincaré duality for analytic $D$-modules, generalizing previous work of Bode. Finally, we relate the theory of analytic $D$-modules to previous work of the author with Rodrigues Jacinto on solid locally analytic representations of $p$-adic Lie groups. |
| title | The analytic de Rham stack in rigid geometry |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2401.07738 |