Holonomicity without Frobenius structure
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.
scientific article; zbMATH DE number 6018605
scientific article