Regular singular differential equations and free proalgebraic groups
Michael Wibmer
TL;DR
This paper identifies the differential Galois group of all regular singular differential equations on the Riemann sphere as a free proalgebraic group with a set of cardinality equal to the complex numbers.
Contribution
It establishes that the differential Galois group for this family is a free proalgebraic group on an uncountably infinite set, providing a complete characterization.
Findings
Differential Galois group is a free proalgebraic group.
The group has cardinality equal to the continuum.
Complete description of the Galois group for regular singular equations.
Abstract
We determine the differential Galois group of the family of all regular singular differential equations on the Riemann sphere. It is the free proalgebraic group on a set of cardinality .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Nonlinear Waves and Solitons · Advanced Algebra and Geometry