{
  "id": "1310.4469",
  "version": "v1",
  "published": "2013-10-16T18:23:08.000Z",
  "updated": "2013-10-16T18:23:08.000Z",
  "title": "The p-cohomology of algebraic varieties and special values of zeta functions",
  "authors": [
    "James S. Milne",
    "Niranjan Ramachandran"
  ],
  "comment": "Because of font differences, the pagination of the arXiv version is different from other versions",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The p-cohomology of an algebraic variety in characteristic p lies naturally in the category $D_{c}^{b}(R)$ of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Illusie-Raynaud). We study homological algebra in this category. When the base field is finite, our results provide relations between the the absolute cohomology groups of algebraic varieties, log varieties, algebraic stacks, etc. and the special values of their zeta functions. These results provide compelling evidence that $D_{c}^{b}(R)$ is the correct target for p-cohomology in characteristic p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-16T18:23:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G15",
      "11G25"
    ],
    "keywords": [
      "algebraic variety",
      "zeta functions",
      "special values",
      "p-cohomology",
      "absolute cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4469M"
    }
  }
}