Vector fields and flows on $C^\infty$-schemes
Eugene Lerman
Published: 2025/3/24
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.