p-adic differential equations over Berkovich curves

Andrea Pulita (U Grenoble Alpes)

Oct 14. 2024, 15:30 — 16:45

We propose to discuss (a selection of) the following items:

An introduction to the basic ideas of Berkovich spaces and why they are a powerful tool in non-Archimedean geometry and in particular in the topic of p-adic differential equations.

Discussing the importance of radii of convergence of solutions to p-adic differential equations and their implications.

Presenting some local and global decomposition theorems that apply to p-adic differential equations. This is similar to the decomposition theorem of a differential equation over C((x)) by the slopes of its Newton Polygon. In fact, this is a particular case of a more general theorem.

An overview of the finite-dimensionality results for the de Rham cohomology associated with these equations. The fact that contrary to the algebraic case, they do not always have a finite dimensional de Rham cohomology and the information about the cohomology is encoded in the radii.ns.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Files:
Slides
Associated Event:
Algebraicity and Transcendence for Singular Differential Equations (Workshop)
Organizer(s):
Alin Bostan (INRIA Paris)
Francis Brown (U Oxford)
Herwig Hauser (U of Vienna)
Shihoko Ishii (U Tokyo)
Hiraku Kawanoue (Chubu U, Kasugai City)
Michael Singer (NC State U, Raleigh)