On the stability of the holonomicity without Frobenius structure: the case of curves

TL;DR

This paper proves that for smooth curves, the stability of holonomicity holds without Frobenius structure under certain conditions, extending Berthelot's conjecture.

Contribution

It demonstrates the stability of holonomicity for smooth curves without Frobenius structure using Christol and Mebkhout's theorem, under non-Liouville hypotheses.

Findings

Holonomicity remains stable without Frobenius structure for smooth curves.

The proof relies on Christol and Mebkhout's algebrization and finiteness theorem.

The result confirms Berthelot's conjecture in this specific setting.

Abstract

By using Christol and Mebkhout's algebrization and finiteness theorem, we prove that in the case of smooth curves, Berthelot's strongest conjecture on the stability of holonomicity is still valid without Frobenius structure but under some non-Liouville type hypotheses.