Vector fields and flows on $C^\infty$-schemes
Differential Geometry
2025-09-10 v2
Abstract
We prove that a vector field on an affine -scheme Spec(A) has a flow if the -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 -schemes.
Keywords
Cite
@article{arxiv.2503.19064,
title = {Vector fields and flows on $C^\infty$-schemes},
author = {Eugene Lerman},
journal= {arXiv preprint arXiv:2503.19064},
year = {2025}
}
Comments
v2: 31 pages. Added a construction of the groupoid integrating the flow. v1: 24 pages. Comments welcome