Submission date: 30 July 2024

Abstract:

Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of precategorical descent applied to algebraic-geometric situations, we develop a Galois theory that applies to morphisms of differential schemes, and vastly generalises the linear Picard-Vessiot theory, as well as the strongly normal theory of Kolchin.

Mathematics Subject Classification: 12H05, 18F20, 18D40, 18E50, 14L30

Keywords and phrases:

Full text arXiv 2407.21147: pdf, ps.