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Mathematics > Algebraic Geometry

arXiv:1807.09317 (math)
[Submitted on 24 Jul 2018 (v1), last revised 30 Jul 2018 (this version, v2)]

Title:Differential Weil Descent and Differentially Large Fields

Authors: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.
Comments: 26 pages
Subjects: Algebraic Geometry (math.AG); Logic (math.LO); Rings and Algebras (math.RA)
MSC classes: 12H05
Cite as: arXiv:1807.09317 [math.AG]
  (or arXiv:1807.09317v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.09317

Submission history

From: Marcus Tressl [view email]
[v1] Tue, 24 Jul 2018 19:40:37 UTC (37 KB)
[v2] Mon, 30 Jul 2018 09:42:15 UTC (38 KB)
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