A Tangent Category Perspective on Connections in Algebraic Geometry
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915028426293248 |
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| author | Cruttwell, G. S. H. Lemay, Jean-Simon Pacaud Vandenberg, Elias |
| author_facet | Cruttwell, G. S. H. Lemay, Jean-Simon Pacaud Vandenberg, Elias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Tangent Category Perspective on Connections in Algebraic Geometry Cruttwell, G. S. H. Lemay, Jean-Simon Pacaud Vandenberg, Elias Category Theory 18F40, 53C05 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. |
| title | A Tangent Category Perspective on Connections in Algebraic Geometry |
| topic | Category Theory 18F40, 53C05 |
| url | https://arxiv.org/abs/2406.15137 |