Galois theory of differential schemes
Algebraic Geometry
2025-10-15 v2 Commutative Algebra
Category Theory
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.
Keywords
Cite
@article{arxiv.2407.21147,
title = {Galois theory of differential schemes},
author = {Ivan Tomašić and Behrang Noohi},
journal= {arXiv preprint arXiv:2407.21147},
year = {2025}
}
Comments
Added the theory of geometric quotients and several applications and examples