{
  "annotation_id": "5cd57af2-a91f-4c48-9979-c87482901de7",
  "date_created": "2026-02-17T05:53:08.663000Z",
  "date_modified": "2026-02-17T05:53:08.663000Z",
  "file_hash": "90f904ecdc4adea63a28c04c4e0c7b5af720c0f042b349309ecd422c60857658",
  "private": false,
  "record": {
    "abstract": "This article focuses on smooth, projective, and geometrically integral varieties $X$ over a field $k$, whose geometric Picard group $Pic(X_{\\overline{k}})$ is torsion-free. We establish an isomorphism$Br(X)/Br(k) \\simeq Br_{nr}\\bigl(Sym_{X/k}^{n}\\bigr)/Br(k)$, where $Sym_{X/k}^{n}$ denotes the $n$-th symmetric product. Using this isomorphism, we investigate the relationship between the Brauer--Manin obstruction to the Hasse principle and weak approximation for rational points on the smooth proejctive model $Sym_{X/k}^{n,sm}$, and the corresponding obstruction for $0$-cycles of degree $n$ on $X$.",
    "arxiv_id": "2601.06872",
    "authors": [
      "Yongqi Liang",
      "Xingyu Liu",
      "Hui Zhang"
    ],
    "categories": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The Brauer-Manin obstruction of Symmetric products",
    "url": "https://arxiv.org/abs/2601.06872",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ed693211-8064-4769-a97e-fe8c4e566b2a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}