Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912669205790720 |
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| author | Jarra, Manoel |
| author_facet | Jarra, Manoel |
| contents | We introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its strong congruence space and the complex toric variety associated to its fan have the same dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15953 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry Jarra, Manoel Algebraic Geometry We introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its strong congruence space and the complex toric variety associated to its fan have the same dimension. |
| title | Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2305.15953 |