Complex analytic vanishing cycles for formal schemes

Given a nonzero complex analytic function defined in a neighborhood of a point in a complex
analytic space and equal to zero at the point, there are associated integral vanishing cycles
cohomology groups. They are finitely generated abelian groups provided with a quasi-unipotent
action of the fundamental group of the punctured complex plane. I will explain results which
imply that those groups depend only on the formal completion of the local ring of the point.
One can in fact extend the construction of those groups to arbitrary nonzero elements of the
maximal ideal of the formal completion and, more generally, to a broad class of formal schemes
over the formal completion of the ring of convergent power series at zero of the complex plane.