Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• Main Author: van der Put, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210224
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic / M. van der Put // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 20 назв. — англ.

Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are a few explicit examples of stratifications. The main goal of this paper is to construct stratifications on projective or affine curves in positive characteristic and to determine the possibilities for their differential Galois groups. For the related "differential Abhyankar conjecture", we present partial answers, supplementing the literature. The tools for the construction of regular singular stratifications and the study of their differential Galois groups are p-adic methods and rigid analytic methods using Mumford curves and Mumford groups. These constructions produce many stratifications and differential Galois groups. In particular, some information on the tame fundamental groups of affine curves is obtained.