Equivariant vector bundles on toric schemes over semirings

Abstract

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 vector bundle on a toric scheme $X$ over an idempotent semifield equivariantly splits as a sum of toric line bundles. We then study the equivariant Picard group ${\text{Pic}}_G(X)$. Finally, we prove a version of Klyachko's classification theorem for toric vector bundles over an idempotent semifield.

References in corpus (5)

• Equations of tropical varieties
• Moduli of toric vector bundles
• Boolean Witt vectors and an integral Edrei-Thoma theorem
• Positive structures in Lie theory
• Tropical Vector Bundles