5 research outputs found
Iterative differential Galois theory: a model theoretic approach
This paper introduces a natural extension of Kolchin's differential Galois
theory to positive characteristic iterative differential fields, generalizing
to the non-linear case the iterative Picard-Vessiot theory recently developed
by Matzat and van der Put. We use the methods and framework provided by the
model theory of iterative differential fields. We offer a definition of
strongly normal extension of iterative differential fields, and then prove that
these extensions have good Galois theory and that a G-primitive element theorem
holds. In addition, making use of the basic theory of arc spaces of algebraic
groups, we define iterative logarithmic equations, finally proving that our
strongly normal extensions are Galois extensions for these equations
Order one differential equations on nonisotrivial algebraic curves
In this paper we provide new examples of geometrically trivial strongly
minimal differential algebraic varieties living on nonisotrivial curves over
differentially closed fields of characteristic zero. Our technique involves
developing a theory of Kodaira-Spencer forms and building connections to
deformation theory. In our development, we answer several open questions posed
by Rosen and some natural questions about Manin kernels.Comment: arXiv admin note: text overlap with arXiv:1707.0871