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We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0. Relying on work of the second author who investigated its properties on affinoid domains of the affine line, we prove that its slopes give rise to continuous functions that factorize by the retraction through a locally finite subgraph of the curve.
We prove that the radii of convergence of the solutions of a $p$-adic differential equation $mathcal{F}$ over an affinoid domain $X$ of the Berkovich affine line are continuous functions on $X$ that factorize through the retraction of $XtoGamma$ of $
We study the radius of convergence of a differential equation on a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0. Several properties of this function are known: F. Baldassarri proved that it is continuous and
We deal with locally free $mathcal{O}_X$-modules with connection over a Berkovich curve $X$. As a main result we prove local and global decomposition theorems of such objects by the radii of convergence of their solutions. We also derive a bound of t
Let $X$ be a quasi-smooth Berkovich curve over a field of characteristic $0$ and let $mathscr{F}$ be a locally free $mathscr{O}_{X}$-module with connection. In this paper, we prove local and global criteria to ensure the finite-dimensionality of the
We show that if a differential equations $mathscr{F}$ over a quasi-smooth Berkovich curve $X$ has a certain compatibility condition with respect to an automorphism $sigma$ of $X$, and if the automorphism is sufficiently close to the identity, then $m