{
  "id": "1308.0472",
  "version": "v1",
  "published": "2013-08-02T11:36:01.000Z",
  "updated": "2013-08-02T11:36:01.000Z",
  "title": "Albanese and Picard 1-Motives in Positive Characteristic",
  "authors": [
    "Peter Mannisto"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We define 1-motives of a variety X over a perfect field of positive characteristic which realize the etale cohomology groups of X in dimension and codimension one. This is the analogue in positive characteristic of previous results of Barbieri-Viale and Srinivas, except that we only consider the etale realization but also consider compactly supported cohomology. The dimension-1 case (called the Picard 1-motives) can be done by standard techniques, and indeed this case is probably well known. But the codimension-one case (Albanese 1-motive) requires stronger tools, namely a strong version of de Jong's alterations theorem and some cycle class theory on smooth Deligne-Mumford stacks which may be of independent interest. Unfortunately, we only succeed in defining the Albanese 1-motive for a variety X over an algebraically closed base field, and only up to isogeny. As a corollary to our definition of these 1-motives we deduce some independence of l results when X is a variety over a finite field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-02T11:36:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F20",
      "14G10"
    ],
    "keywords": [
      "positive characteristic",
      "smooth deligne-mumford stacks",
      "cycle class theory",
      "jongs alterations theorem",
      "etale cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0472M"
    }
  }
}