Holonomic D-cap-modules on rigid analytic spaces

2025/12/09 by Bode, Andreas
#14F10 #14G22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.08838

Abstract

We adapt Caro's notion of overholonomicity to give a definition of holonomic D-cap-modules on rigid analytic spaces. We prove stability under five of the six operations (both inverse image functors, duality, and both direct image functors for projective morphisms), as well as base change results. Up to the open problem of stability under tensor products, we obtain an analogue of the usual six-functor formalism for holonomic D-modules.

Citations

• Six-Functor Formalisms
• Analytic de Rham stacks of Fargues-Fontaine curves
• Auslander regularity of completed rings of p-adic differential operators
• Six operations for D-cap-modules on rigid analytic spaces
• Extending meromorphic connections to coadmissible D-cap-modules
• A Proper Mapping Theorem for coadmissible D-cap-modules
• D-modules on rigid analytic spaces II: Kashiwara's equivalence
• D-modules on rigid analytic spaces
• On irreducible representations of compact p-adic analytic groups
• Functorial desingularization over Q: boundaries and the embedded case
• Overholonomicity of overconvergent F-isocrystals over smooth varieties

Cited by

• Characteristic cycles for coadmissible D-modules on smooth rigid analytic curves

Related

• D-modules on rigid analytic spaces III: Weak holonomicity and operations
• Six operations for D-cap-modules on rigid analytic spaces
• D-modules on rigid analytic spaces II: Kashiwara's equivalence
• Holonomic \mathscrD-modules on rigid analytic varieties
• A Proper Mapping Theorem for coadmissible D-cap-modules