29 citations · 185 across the 37 of their papers we have counts for
21 papers · 1 filter
Two comparison theorems for semiring schemes
Oliver Lorscheid
In this note, we compare the two approaches to semiring schemes as topological spaces with a structure sheaf and as a functor of points. We explain and prove the following two resu…
Toolkit for the algebraic geometer
Sourayan Banerjee, Oliver Lorscheid, Alejandro Martínez Méndez +1
In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, a…
Tropical geometry over the tropical hyperfield
Oliver Lorscheid
In this text, we merge ideas around the tropical hyperfield with the theory of ordered blueprints to give a new formulation of tropical scheme theory. The key insight is that a non…
Higher balancing for locally tropically convex tropical varieties
Emilio Assemany, Oliver Lorscheid
In this text, we show that locally tropically convex tropical varieties in have locally a canonical polyhedral structure that satisfies higher balancing conditions a…
The moduli space of matroids
Matthew Baker, Oliver Lorscheid
In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy…
for everyone
Oliver Lorscheid
This text serves as an introduction to -geometry for the general mathematician. We explain the initial motivations for -geometry in detail, provide an o…