The variation of the radii of convergence of linear p-adic differential equations

BIMSA-YMSC Number Theory Lunch Seminar

Organizers：

Yong Suk Moon, Koji Shimizu

Speaker：

Tinhinane Azzouz (BIMSA)

Time：

Thur., 12:00-13:00, Nov. 6, 2025

Venue：

BIMSA A4-1

Title:

The variation of the radii of convergence of linear p-adic differential equations

Abstract:

This talk explores the behavior of p-adic differential equations as the base point varies along the skeleton of an annulus. In the first part, we study how Newton polygons change when the norms of the coefficients vary, with these norms corresponding to the position of the point on the skeleton. This affects the slopes of the polygon and encodes the local behavior of solutions. In the second part, we examine how radii of convergence vary with the point, explain why this variation is continuous, and highlight several remarkable properties they satisfy.