{
  "id": "2303.13725",
  "version": "v1",
  "published": "2023-03-24T00:33:23.000Z",
  "updated": "2023-03-24T00:33:23.000Z",
  "title": "Explicit bounds on torsion of CM abelian varieties over $p$-adic fields with values in Lubin-Tate extensions",
  "authors": [
    "Yoshiyasu Ozeki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ and $k$ be $p$-adic fields. Let $L$ be the composite field of $K$ and a certain Lubin-Tate extension over $k$ (including the case where $L=K(\\mu_{p^{\\infty}})$). In this paper, we show that there exists an explicitly described constant $C$ in terms of some invariants of $K,k$ and an integer $g \\ge 1$ which satisfies the following property: If $A_{/K}$ is a $g$-dimensional CM abelian variety, then the order of the $p$-torsion subgroup of $A(L)$ is bounded by $C$. We also give a similar bound in the case where $L=K(\\sqrt[p^{\\infty}]{K})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-24T00:33:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic fields",
      "lubin-tate extension",
      "explicit bounds",
      "dimensional cm abelian variety",
      "composite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}