Cartan's proof for the Darboux theorem in <i>A</i>-modules

Abstract

We refer to [4] for a proof of the (affine) Darboux theorem in the category A-ModX of A-modules, defined on a fixed topological space X. Hereby, we present another proof of the same theorem, based on E. Cartan’s approach, keeping, as is done in [4], the condition affixed to the coefficient algebra sheaf A, that is, A satisfies the inverse-closed section condition.

Quaestiones Mathematicae 35(2012), 259–264.