Differential Galois groups, specializations and Matzat's conjecture

2022/09/04 by Feng, Ruyong, Wibmer, Michael
#12H05 #14L15 #34M50 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.01581

Abstract

We study families of linear differential equations parametrized by an algebraic variety X and show that the set of all points x∈ 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 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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