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arXiv · 2209.01581

Differential Galois groups, specializations and Matzat's conjecture

Ruyong Feng·Michael Wibmer
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Abstract

We study families of linear differential equations parametrized by an algebraic variety $\mathcal{X}$ and show that the set of all points $x\in \mathcal{X}$, such that the differential Galois group at the generic fibre specializes to the differential Galois group at the fibre over $x$, is Zariski dense in $\mathcal{X}$. As an application, we prove Matzat's conjecture in full generality: The absolute differential Galois group of a one-variable function field over an algebraically closed field of characteristic zero is a free proalgebraic group.

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Ruyong Feng, Michael Wibmer. 2022-09-04. Differential Galois groups, specializations and Matzat's conjecture. https://arxiv.org/abs/2209.01581

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