A Tangent Category Perspective on Connections in Algebraic Geometry
Category Theory
2024-11-22 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2406.15137,
title = {A Tangent Category Perspective on Connections in Algebraic Geometry},
author = {G. S. H. Cruttwell and Jean-Simon Pacaud Lemay and Elias Vandenberg},
journal= {arXiv preprint arXiv:2406.15137},
year = {2024}
}
Comments
Minor changes and typos fixes based on reviewer comments