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Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic

Van der Put, M., 2019, In : Symmetry, Integrability and Geometry. 15, 24 p., 071.

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  • Stratified Bundles on Curves and Differential Galois Groups in Positive Characteristic

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  • Marius Van der Put

Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are 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.

Original languageEnglish
Article number071
Number of pages24
JournalSymmetry, Integrability and Geometry
Volume15
Publication statusPublished - 2019

    Keywords

  • stratified bundle, differential equations, positive characteristic, fundamental group, Mumford curve, Mumford group, differential Galois group

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