499 research outputs found
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. These are systems whose
solutions only have binary algebraic relations between them. Our technique
involves developing a theory of -forms, and building connections to
deformation theory. This builds on previous work of Buium and Rosen. In our
development, we answer several open questions posed by Rosen and
Hrushovski-Itai
Arithmetic Deformation Classes Associated to Curves via p-Jet Spaces
We show that for certain curves over p-adic rings its first p-jet space admits the structure of a torsor under a line bundle
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