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arXiv · 2305.15953

Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry

Manoel Jarra
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Abstract

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.

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Manoel Jarra. 2023-05-25. Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry. https://doi.org/10.1016/j.jpaa.2025.107862

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