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

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-24
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

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

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

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

article en

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.

ArXiv.org
Openalex Percentile: Top 44%
Homotopy and Cohomology in Algebraic Topology
Open Access PDFOpenAlex
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Vector fields and flows on $C^\infty$-schemes · ArXiv.org (2025) | TGRS Research Map | TGRS