Tropical cohomology for band schemes over the tropical hyperfield

Seungkyu Lee

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arXiv · 2610.32016

Tropical cohomology for band schemes over the tropical hyperfield

Seungkyu Lee

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Abstract

We define tropical band varieties as $\mathbf{T}$-reductions of separated finitely presented $\mathbf{T}$-band schemes. We construct a faithful functor from the category of tropical band varieties to the category of extended polyhedral spaces in the sense of Gross--Shokrieh. As a byproduct, we show that tropical cohomology can be defined functorially on tropical band varieties.

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Seungkyu Lee. 2026-10-23. Tropical cohomology for band schemes over the tropical hyperfield. https://arxiv.org/abs/2610.32016

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