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Equivariant vector bundles on toric schemes over semirings
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 28 July 2025, pp. 1-67
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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
$\operatorname{Pic}_G(X)$. Finally, we prove a version of Klyachko’s classification theorem for toric vector bundles over an idempotent semifield.
