{
  "id": "0909.4806",
  "version": "v1",
  "published": "2009-09-25T21:22:31.000Z",
  "updated": "2009-09-25T21:22:31.000Z",
  "title": "On the reduction of points on abelian varieties and tori",
  "authors": [
    "Antonella Perucca"
  ],
  "comment": "12 pages; comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let G be the product of an abelian variety and a torus defined over a number field K. Let R_1,..., R_n be points in G(K). Let l be a rational prime and let a_1,..., a_n be non-negative integers. Consider the set of primes p of K satisfying the following condition: the l-adic valuation of the order of (R_i mod p) equals a_i for every i=1,...,n. We show that this set has a natural density and we characterize the n-tuples a_1,..., a_n for which the density is positive. More generally, we study the l-part of the reduction of the points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-25T21:22:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "number field",
      "l-adic valuation",
      "natural density",
      "rational prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4806P"
    }
  }
}