{
  "id": "2406.06933",
  "version": "v1",
  "published": "2024-06-11T04:15:13.000Z",
  "updated": "2024-06-11T04:15:13.000Z",
  "title": "Equivariant vector bundles on toric schemes over semirings",
  "authors": [
    "Jaiung Jun",
    "Kalina Mincheva",
    "Jeffrey Tolliver"
  ],
  "categories": [
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-11T04:15:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A23",
      "14T10",
      "14C22"
    ],
    "keywords": [
      "equivariant vector bundles",
      "toric scheme",
      "toric vector bundle",
      "idempotent semifield equivariantly splits",
      "klyachkos classification theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}