A differential Chevalley theorem

Details A differential Chevalley theorem A differential Chevalley theorem

2008-10-30

arxiv.org/abs/0810.5486v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a differential scheme under a finite morphism is a constructible set. We also obtain a new algebraic characterization of differentially closed fields. We show that similar results hold for differentially closed fields that are saturated, in the sense of model theory. In characteristic p > 0, we obtain related results and establish a differential Nullstellensatz. Analogs of these theorems for difference fields are also considered.

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