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Subgroups of free proalgebraic groups and Matzat's conjecture for function fields

We show that a closed finite index subgroup of a free proalgebraic group is itself a free proalgebraic group. Our main motivation for this result is an application in differential Galois theory: The absolute differential Galois group of a one-variable function field is a free proalgebraic group.

preprint2021arXivOpen access
Michael Wibmer
math.ACmath.GR
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Michael Wibmer

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