Spectrum of p-adic linear differential equations

Abstract

This paper generalizes our works in [Azz20] and [Azz21], which concern the determination of the spectrum in the sense of Berkovich of ultrametric linear differential equations, in the special cases with constant coefficients or over a field of formal power series. In this paper, we determine the spectrum of any p-adic differential equation. This permits to establish a strong link between the spectrum and all the radii of convergence of a differential equation. Moreover, the spectrum provides a finer decomposition than Robba's decomposition by spectral radii [Rob75].Comment: 45 pages. The comments are welcom