Cut-by-curves criterion for the overconvergence of p-adic differential equations

TL;DR

This paper introduces a new criterion based on cut-by-curves to determine the overconvergence of p-adic differential equations, aiding in understanding their analytic properties over p-adic fields.

Contribution

It establishes a novel cut-by-curves criterion for overconvergence of integrable connections on rigid analytic spaces and p-adic varieties, advancing the theoretical framework.

Findings

Proves the cut-by-curves criterion for overconvergence.

Applies the criterion to specific rigid analytic spaces.

Enhances understanding of p-adic differential equations.

Abstract

In this paper, we prove a `cut-by-curves criterion' for the overconvergence of integrable connections on certain rigid analytic spaces and certain varieties over $p$-adic fields.