The analytic de Rham stack in rigid geometry

Rodríguez Camargo, Juan Esteban

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The analytic de Rham stack in rigid geometry

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Rodríguez Camargo, Juan Esteban
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2401.07738
(Preprint)

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2401.07738.pdf
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Citation

Rodríguez Camargo, J. E. (submitted). The analytic de Rham stack in rigid geometry.

Cite as: https://hdl.handle.net/21.11116/0000-000F-54BC-F

Abstract

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.