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arXiv · 1904.07806

Free differential Galois groups

Annette Bachmayr·David Harbater·Julia Hartmann·Michael Wibmer
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Abstract

We study the structure of the absolute differential Galois group of a rational function field over an algebraically closed field of characteristic zero. In particular, we relate the behavior of differential embedding problems to the condition that the absolute differential Galois group is free as a proalgebraic group. Building on this, we prove Matzat's freeness conjecture in the case that the field of constants is algebraically closed of countably infinite transcendence degree over the rationals. This is the first known case of the twenty year old conjecture.

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Annette Bachmayr, David Harbater, Julia Hartmann, Michael Wibmer. 2019-04-16. Free differential Galois groups. https://arxiv.org/abs/1904.07806

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