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A Tangent Category Perspective on Connections in Algebraic Geometry

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arxiv 2406.15137 v2 pith:2G2NUE6X submitted 2024-06-21 math.CT

G.S.H. Cruttwell , Jean-Simon Pacaud Lemay , Elias Vandenberg This is my paper · ORCID
classification math.CT
keywords categorytangentconnectionnotionconnectionsrecreatesschemesthere
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There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical notion of a connection on a module (and similarly, in the tangent category of schemes, this recreates the notion of connection on a quasi-coherent sheaf of modules). By contrast, we also show that in the tangent category of algebras, there are no non-trivial connections.

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