Solid Arithmetic D-modules

We introduce a solid ring of arithmetic differential operators analogue to Berthelot's D-dagger, and its derived infinity-category of solid quasi-coherent modules. We show that there is a fully faithful functor from Berthelot's derived category of bounded complexes of D-dagger-modules with coherent cohomology into our new category.

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Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39799
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

Solid Arithmetic D-modules

Kolar David
arXiv (Cornell University)
Algebraic Geometry and Number Theory
preprint

Solid Arithmetic D-modules

Kolar David
preprint en

Abstract

We introduce a solid ring of arithmetic differential operators analogue to Berthelot's D-dagger, and its derived infinity-category of solid quasi-coherent modules. We show that there is a fully faithful functor from Berthelot's derived category of bounded complexes of D-dagger-modules with coherent cohomology into our new category.

arXiv (Cornell University)
Institut de recherche mathématique de Rennes (FR)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Solid Arithmetic D-modules — Kolar David · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS