Tropical cohomology for band schemes over the tropical hyperfield

Source 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.