We introduce a scheme-theoretic enrichment of the principal objects of tropical geometry.
Using a category of semiring schemes, we construct tropical hypersurfaces as schemes over …

We contribute to the foundations of tropical geometry with a view toward formulating tropical
moduli problems, and with the moduli space of curves as our main example. We propose a …

Given an integral scheme $ X $ over a non-archimedean valued field $ k $, we construct a
universal closed embedding of $ X $ into a $ k $-scheme equipped with a model over the …

We study linear degenerations of flag varieties from the point of view of tropical geometry.
We define the linear degenerate flag Dressian and prove a correspondence between: $(a) …

The goal of this paper is to introduce a construction of a vector bundle on a tropical variety.
When the base is a tropical toric variety these tropicalize toric vector bundles, and are …

In this paper we introduce congruence spaces, which are topological spaces that are
canonically attached to monoid schemes and that reflect closed topological properties. This …

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Using the notion of a root datum of a reductive group G we propose a tropical analogue of a
principal G-bundle on a metric graph. We focus on the case G= GL n, ie the case of vector …

Abstract Tropical ideals, introduced in [12], define subschemes of tropical toric varieties. We
prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of …

We prove a fundamental theorem for tropical partial differential equations analogue of the
fundamental theorem of tropical geometry in this context. We extend results from Aroca et al …