Spectrum of a linear differential equation over a field of formal power series

Tinhinane Amina Azzouz (1)

1 IF - Institut Fourier

In this paper we associate to a linear differential equation with coefficients in the field of Laurent formal power series a new geometric object, a spectrum in the sense of Berkovich. We will compute this spectrum and show that it contains interesting informations about the equation.

Mots clés: Formal differential equations; Berkovich analytic spaces; Spectral theory

Domaines: Théorie des nombres [math.NT]; Théorie spectrale [math.SP]

Tinhinane Amina Azzouz. Spectrum of a linear differential equation over a field of formal power series. 2019. ⟨hal-01853797⟩