{
  "id": "0711.1928",
  "version": "v7",
  "published": "2007-11-13T20:44:02.000Z",
  "updated": "2019-02-05T17:14:32.000Z",
  "title": "Duality of Anderson T-motives",
  "authors": [
    "A. Grishkov",
    "D. Logachev"
  ],
  "comment": "53 pages. Minor corrections",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $M$ be a T-motive. We introduce the notion of duality for $M$. Main results of the paper (we consider uniformizable $M$ over $F_q[T]$ of rank $r$, dimension $n$, whose nilpotent operator $N$ is 0): 1. Algebraic duality implies analytic duality (Theorem 5). Explicitly, this means that the lattice of the dual of $M$ is the dual of the lattice of $M$, i.e. the transposed of a Siegel matrix of $M$ is a Siegel matrix of the dual of $M$. 2. Let $n=r-1$. There is a 1 -- 1 correspondence between pure T-motives (all they are uniformizable), and lattices of rank $r$ in $C^n$ having dual (Corollary 8.4).",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-01-09T14:45:03.000Z",
      "comment": "51 pages. Minor renovations and corrections",
      "journal": null,
      "doi": null,
      "authors": [
        "D. Logachev"
      ]
    },
    {
      "version": "v7",
      "updated": "2019-02-05T17:14:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G09",
      "11G15",
      "14K22"
    ],
    "keywords": [
      "anderson t-motives",
      "algebraic duality implies analytic duality",
      "siegel matrix",
      "main results",
      "nilpotent operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1928L"
    }
  }
}