We introduce tropical spectrahedra, defined as the images by the nonarchimedean
valuation of spectrahedra over the field of real Puiseux series. We provide an explicit …

The symmetrized tropical semiring is an extension of the tropical semifield, initially
introduced to solve tropical linear systems using Cramer's rule. It is equivalent to the real …

Let I be an ideal of the ring of Laurent polynomials K [x 1±1,…, xn±1] with coefficients in a
real-valued field (K, v). The fundamental theorem of tropical algebraic geometry states the …

A coamoeba is the image of a subvariety of a complex torus under the argument map to the
real torus. Similarly, a non-archimedean coamoeba is the image of a subvariety of a torus …

We show that the tropicalization of a connected variety over a higher rank valued field is a
path connected topological space. This establishes an affirmative answer to a question …

In this paper we propose a general functorial definition of the operation of\emph {local
tropicalization} in commutative algebra. Let $ R $ be a commutative ring, $\Gamma $ a …

We introduce the tropicalization of closed sub-schemes of a torus defined over a higher
dimensional local field. We study the basic invariants of such tropicalizations. This is a …

We develop a theory of multistage degenerations of toric varieties over finite rank valuation
rings, extending the Mumford–Gubler theory in rank 1. Such degenerations are constructed …

We propose to study the tropical geometry specifically arising from convergent Hahn series
in multiple indeterminates. One application is a new view on stable intersections of tropical …

Higher rank Voronoi tilings Page 1 HIGHER RANK INNER PRODUCTS, VORONOI TILINGS
AND METRIC DEGENERATIONS OF TORI OMID AMINI AND NOEMA NICOLUSSI Abstract …