English

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

Differential Geometry 2025-09-10 v2

Abstract

We prove that a vector field on an affine CC^\infty-scheme Spec(A) has a flow if the CC^\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 CC^\infty-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

R2 v1 2026-06-28T22:32:56.708Z