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arXiv · 1807.09317

Differential Weil Descent and Differentially Large Fields

Omar León Sánchez·Marcus Tressl
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Abstract

A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then used to prove that in characteristic 0, \textit{differential largeness} (a notion introduced here as an analogue to largeness of fields) is preserved under algebraic extensions. This provides many new differential fields with minimal differential closures. A further application is Kolchin-density of rational points in differential algebraic groups defined over differentially large fields.

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Omar León Sánchez, Marcus Tressl. 2018-07-24. Differential Weil Descent and Differentially Large Fields. https://arxiv.org/abs/1807.09317

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