Holonomicity without Frobenius structure
type: Item
instance of: scholarly article
title: Holonomicity without Frobenius structure
zbMATH Open document ID: 1300.14022
author: Daniel Caro
publication date: 2012-03-28T00:00:00Z
full work available at URL: https://eudml.org/doc/219673
review text: The author deals with the definition of holonomy for arithmetic \(\mathcal D\)-modules. This notion, defined this way, does not need the presence of a Frobenius structure as defined by \textit{P. Berthelot} [Astérisque 279, 1--80 (2002; Zbl 1098.14010)] although both definitions coincide when having such an structure. It is also proven that this definition verifies the Bernstein's inequality and the duality criterion, as in the context of classical \(\mathcal D\)-modules. In the last two sections, the author provides a new holonomy criterion using the notion of overcoherence.
reviewed by: Alberto Castaño Domínguez
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14F30
zbMATH DE Number: 6018605
zbMATH Keywords: holonomy
zbMATH Keywords: arithmetic \(\mathcal D\)-modules
MaRDI profile type: Publication
OpenAlex ID: W2324730186
cites work: Q3209229
cites work: ${\scr D}$-modules arithmétiques. I. Opérateurs différentiels de niveau fini
cites work: ${\cal D}$-modules arithmétiques. II: Descente par Frobenius
cites work: Q4539739
cites work: Q3325851
cites work: Overcoherent arithmetic \(\mathcal D\)-modules. Application to \(L\)-functions.
cites work: Comparing the sheaves of overconvergent isocrystals
cites work: Devissage of the \(F\)-complexes of arithmetic \(\mathcal D\)-modules in overconvergent \(F\)-isocrystals
cites work: Fonctions L associées aux $\mathcal{D}$-modules arithmétiques. Cas des courbes
cites work: Over convergent \(F\)-isocrystals and differential overcoherence
cites work: $\mathcal{D}$-modules arithmétiques surholonomes
cites work: A characterization of the overcoherence
cites work: Finiteness of the homological dimension of weakly complete algebras of differential operator with overconvergent coefficients
cites work: Dualité locale et holonomie pour les ${\cal D}$-modules arithmétiques
DOI: 10.5802/AIF.2645
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 6018605