Now in its second edition, this volume provides a uniquely detailed study of $ P $-adic
differential equations. Assuming only a graduate-level background in number theory, the text …

We give a criterion under which one can obtain a good decomposition (in the sense of
Malgrange) of a formal flat connection on a complex analytic or algebraic variety of arbitrary …

Given a flat meromorphic connection on an excellent scheme over a field of characteristic
zero, we prove existence of good formal structures after blowing up; this extends a theorem …

We prove a fundamental theorem for tropical partial differential equations analogue of the
fundamental theorem of tropical geometry in this context. We extend results from Aroca et al …

This paper deals with connections on non-archimedean, especially p-adic, analytic curves,
in the sense of Berkovich. The curves must be compact but the connections are allowed to …

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 …

We prove that the radii of convergence of the solutions of ap-adic differential equation F over
an affinoid domain X of the Berkovich affine line are continuous functions on X that factorize …

We consider variational properties of some numerical invariants, measuring convergence of
local horizontal sections, associated to differential modules on polyannuli over a …

The main purpose of this work is to build a refinement of Grigoriev's framework that records
the valuations of the coefficients in a power series solution so that convergence information …

The first aim of this paper is to generalize the results of arXiv: 2111.03548 to the case of
quasi-smooth curves, which consist on providing the link between the spectrum and the radii …