{
  "id": "1401.6847",
  "version": "v3",
  "published": "2014-01-27T13:47:30.000Z",
  "updated": "2016-03-03T13:05:02.000Z",
  "title": "A motivic formula for the L-function of an abelian variety over a function field",
  "authors": [
    "Bruno Kahn"
  ],
  "comment": "Substantially revised. In particular proofs in Section 2 are simplified and clarified, and the motivation for Section 7 is more detailed",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $A$ be an abelian variety over the function field of a smooth projective curve $C$ over an algebraically closed field $k$. We compute the $l$-adic cohomology groups of $C$ with coefficients in the locally constant sheaf associated to $H^1(\\bar A,\\mathbf{Q}_l)$ in terms of arithmetico-geometric invariants of $A$. We apply this, when $k$ is the algebraic closure of a finite field, to a motivic computation of the $L$-function of $A$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-04T16:44:57.000Z",
      "abstract": "Let A be an abelian variety over the function field of a smooth projective curve C over an algebraically closed field k. We compute the l-adic cohomology groups of C with coefficients in the locally constant sheaf associated to H^1(\\bar A,Q_l) in terms of arithmetico-geometric invariants of A. We apply this, when k is the algebraic closure of a finite field, to a motivic computation of the L-function of A.",
      "comment": "Minor changes, renumbering of introduction",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-03-03T13:05:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "function field",
      "motivic formula",
      "l-function",
      "l-adic cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6847K"
    }
  }
}