{
  "id": "2406.05674",
  "version": "v1",
  "published": "2024-06-09T07:07:25.000Z",
  "updated": "2024-06-09T07:07:25.000Z",
  "title": "Splitting of abelian varieties in motivic stable homotopy category",
  "authors": [
    "Haoyang Liu"
  ],
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "In this paper, we discuss the motivic stable homotopy type of abelian varieties. For an abelian variety over a field $k$ with a rational point, it always splits off a top-dimensional cell in motivic stable homotopy category $\\text{SH}(k)$. Let $k = \\mathbb{R}$, there is a concrete splitting which is determined by the motive of X and the real points $X(\\mathbb{R})$ in $\\text{SH}(\\mathbb{R})_\\mathbb{Q}$. We will also discuss this splitting from a viewpoint of the Chow-Witt correspondences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-09T07:07:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "motivic stable homotopy category",
      "abelian variety",
      "motivic stable homotopy type",
      "rational point",
      "top-dimensional cell"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}