{
  "id": "2010.03301",
  "version": "v1",
  "published": "2020-10-07T09:27:18.000Z",
  "updated": "2020-10-07T09:27:18.000Z",
  "title": "On the cohomology of reciprocity sheaves",
  "authors": [
    "Federico Binda",
    "Kay Rülling",
    "Shuji Saito"
  ],
  "comment": "116 pages, comments welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we show the existence of an action of Chow correspondences on the cohomology of reciprocity sheaves. In order to do so, we prove a number of structural results, such as a projective bundle formula, a blow-up formula, a Gysin sequence, and the existence of proper pushforward. In this way we recover and generalize analogous statements for the cohomology of Hodge sheaves and Hodge-Witt sheaves. Among the applications, we construct new birational invariants of smooth projective varieties and obstructions to the existence of zero-cycles of degree one from the cohomology of reciprocity sheaves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-07T09:27:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F43",
      "14F05",
      "14C25"
    ],
    "keywords": [
      "reciprocity sheaves",
      "cohomology",
      "gysin sequence",
      "birational invariants",
      "hodge-witt sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 116,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}