Vector fields and flows on $C^{\infty }$-schemes

Abstract

We prove that a vector field on an affine $C^{\infty }$-scheme Spec(A) has a flow if the $C^{\infty }$-ring A is finitely generated. If the vector field is complete then the flow is the target map of a groupoid internal to the category of $C^{\infty }$-schemes.

v2: 31 pages. Added a construction of the groupoid integrating the flow. v1: 24 pages. Comments welcome