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

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Abstract

We show that a closed finite index subgroup of a free proalgebraic group is itself a free proalgebraic group. As an application, we prove that the absolute differential Galois group of a one-variable function field over an algebraically closed characteristic zero field of infinite transcendence degree is a free proalgebraic group.

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Authors and Affiliations

  1. Institute of Analysis and Number Theory, Graz University of Technology, Kopernikusgasse 24, 8010, Graz, Austria

    Michael Wibmer

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  1. Michael Wibmer
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Correspondence to Michael Wibmer.

Additional information

This work was supported by the NSF grants DMS-1760212, DMS-1760413, DMS-1760448 and the Lise Meitner grant M-2582-N32 of the Austrian Science Fund FWF.

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Wibmer, M. Subgroups of free proalgebraic groups and Matzat’s conjecture for function fields. Isr. J. Math. 253, 841–863 (2023). https://doi.org/10.1007/s11856-022-2383-6

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  • DOI: https://doi.org/10.1007/s11856-022-2383-6

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