  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.

Algebraic Geometry;Logic;Rings and Algebras