arXiv Open Access 2024

The analytic de Rham stack in rigid geometry

Juan Esteban Rodríguez Camargo

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.AG math.RT

Penulis (1)

Juan Esteban Rodríguez Camargo

Format Sitasi

APA MLA BibTeX

Camargo, J.E.R. (2024). The analytic de Rham stack in rigid geometry. https://arxiv.org/abs/2401.07738

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓