Fields with several commuting derivations

David Pierce

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arXiv · 0708.2769

Fields with several commuting derivations

David Pierce

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Abstract

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential fields has a model-companion. The axioms are that certain differential varieties determined by certain ordinary varieties are nonempty. There is no restriction on the characteristic of the underlying field.

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David Pierce. 2007-08-21. Fields with several commuting derivations. https://arxiv.org/abs/0708.2769

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