{
  "id": "2207.03461",
  "version": "v1",
  "published": "2022-07-07T17:42:58.000Z",
  "updated": "2022-07-07T17:42:58.000Z",
  "title": "Regulators in the Arithmetic of Function Fields",
  "authors": [
    "Quentin Gazda"
  ],
  "comment": "Comments are welcome !",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "As a natural sequel for the study of $A$-motivic cohomology, initiated in [Gaz], we develop a notion of regulator for rigid analytically trivial mixed Anderson $A$-motives. In accordance with the conjectural number field picture, we define it as the morphism at the level of extension modules induced by the exactness of the Hodge-Pink realization functor. The purpose of this text is twofold: we first prove a finiteness result for $A$-motivic cohomology and, under a weight assumption, we then show that the source and the target of regulators have the same dimension. It came as a surprise to the author that the image of this regulator might not have full rank, preventing the analogue of a renowned conjecture of Beilinson to hold in our setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-07T17:42:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R58",
      "19E15",
      "11G09"
    ],
    "keywords": [
      "function fields",
      "arithmetic",
      "motivic cohomology",
      "conjectural number field picture",
      "rigid analytically trivial mixed anderson"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}