6533b833fe1ef96bd129c2e8

RESEARCH PRODUCT

Free differential Galois groups

Michael WibmerAnnette BachmayrJulia HartmannDavid Harbater

subject

Rational numberPure mathematicsGroup (mathematics)Applied MathematicsGeneral Mathematics010102 general mathematicsGalois groupField (mathematics)Transcendence degreeMathematics - Commutative AlgebraCommutative Algebra (math.AC)01 natural sciences12H05 12F12 34M50FOS: MathematicsDifferential algebra0101 mathematicsAlgebraically closed fieldPicard–Vessiot theoryMathematics

description

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.

yearjournalcountryeditionlanguage
2019-04-16
https://dx.doi.org/10.48550/arxiv.1904.07806