4 citations · 4 across the 11 of their papers we have counts for
12 papers
Closure operators and geometric modules of valuated matroids
Jaiung Jun, Jeffrey Tolliver
We introduce a closure operator for valuated matroids and prove that it yields a cryptomorphic definition of valuated matroids. As an application, we introduce a class of modules o…
Matroidal representations of low rank
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We study tropical subrepresentations of the Boolean regular representation of a finite group . These are equivalent to the matroids on ground set for which l…
Tropical representations and valuated matroids
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We explore several facets of tropical subrepresentations of a linear representation of a group over the tropical semifield . A key role in the study of tropical subrepr…
Representation theory over semifields
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We study and classify representations of a torsion group over an idempotent semifield with special attention on the case over the Boolean semifield . In subsequent…
Equivariant vector bundles on toric schemes over semirings
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric ve…
Proto-exact categories of modules over semirings and hyperrings
Jaiung Jun, Matt Szczesny, Jeffrey Tolliver
\emph{Proto-exact categories}, introduced by Dyckerhoff and Kapranov, are a generalization of Quillen exact categories which provide a framework for defining algebraic K-theory and…
Vector bundles on tropical schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We define vector bundles for tropical schemes, and explore their properties. The paper largely consists of three parts; (1) we study free modules over zero-sum free semirings, whic…
Lattices, Spectral Spaces, and Closure Operations on Idempotent Semirings
Jaiung Jun, Samarpita Ray, Jeffrey Tolliver
Spectral spaces, introduced by Hochster, are topological spaces homeomorphic to the prime spectra of commutative rings. In this paper we study spectral spaces in perspective of ide…
Picard groups for tropical toric schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
From any monoid scheme (also known as an -scheme) one can pass to a semiring scheme (a generalization of a tropical scheme) by scalar extension to an idempo…
Extension of valuations in characteristic one
Jeffrey Tolliver
We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the wa…
An equivalence between two approaches to limits of local fields
Jeffrey Tolliver
Marc Krasner proposed a theory of limits of local fields in which one relates the extensions of a local field to the extensions of a sequence of related local fields. The key ingre…
Finite Extensions of
Jeffrey Tolliver
We classify the semifields and division semirings containing the max-plus semifield , which are finitely generated as -semimodules…