Beyond perturbation 1: de Rham spaces (Q1742276)

It is known that differential operators can be defined in de Rham spaces constructed in terms of infinitesimal neighborhoods given by nilpotent elements. \textit{I. Moerdijk} and \textit{G. E. Reyes} [J. Algebra 99, 324--336 (1986; Zbl 0592.18005)] noted that besides the usual nilpotent elements, \(C^\infty\)-rings can have \(\infty\)-nilpotent ones. In the paper under review the authors start a theory on the geometry of the resulting de Rham spaces. They find a richer structure obtaining differential operators that go beyond perturbation, i.e., they provide an infinitesimal description of deformations of the identity morphism on a manifold whose infinite jets at the identity vanish.