We introduce stacks classifying \'etale germs of pointed n-dimensional
varieties. We show that quasi-coherent sheaves on these stacks are universal D-
and O-modules. We state and prove a relative version of Artin's approximation
theorem, and as a consequence identify our stacks with classifying stacks of
automorphism groups of the n-dimensional formal disc. We introduce the notion
of convergent universal modules, and study them in terms of these stacks and
the representation theory of the automorphism groups.Comment: 61 pages. Version 1 had a gap: Artin's approximation theorem was
misstated and the incorrect version was used. This gap has been fixed, using
new material in sections 2 and 5. Section 8 has been added, to treat the
dg-categorical version of the results. The paper has been restructured and
the introduction has been expanded. Version 3: minor change