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

Michael Wibmer

doi:10.1007/s11856-022-2383-6

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

Michael Wibmer

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	23
Journal	Israel Journal of Mathematics
Early online date	2022
DOIs	https://doi.org/10.1007/s11856-022-2383-6
Publication status	E-pub ahead of print - 2022

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s11856-022-2383-6

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

Abstract

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