{
  "id": "1205.5945",
  "version": "v2",
  "published": "2012-05-27T07:00:07.000Z",
  "updated": "2013-04-26T09:16:16.000Z",
  "title": "On the Iwasawa Main conjecture of abelian varieties over function fields",
  "authors": [
    "King Fai Lai",
    "Ignazio Longhi",
    "Ki-Seng Tan",
    "Fabien Trihan"
  ],
  "comment": "80 pages; many relevant changes all over the paper from v1. Among the most significant ones: new introduction; proof of the functional equation for Gamma systems in more cases and some applications to CM abelian varieties",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study a geometric analogue of the Iwasawa Main Conjecture for abelian varieties in the two following cases: constant ordinary abelian varieties over $Z_p^d$-extensions of function fields ($d\\geq 1$) ramified at a finite set of places, and semistable abelian varieties over the arithmetic $Z_p$-extension of a function field. One of the tools we use in our proof is a pseudo-isomorphism relating the duals of the Selmer groups of $A$ and its dual abelian variety $A^t$. This holds as well over number fields and is a consequence of a quite general algebraic functional equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-26T09:16:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11S40",
      "11R58",
      "11G10"
    ],
    "keywords": [
      "iwasawa main conjecture",
      "function field",
      "quite general algebraic functional equation",
      "constant ordinary abelian varieties",
      "dual abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 80,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5945L"
    }
  }
}