{
  "id": "2010.04059",
  "version": "v1",
  "published": "2020-10-08T15:24:46.000Z",
  "updated": "2020-10-08T15:24:46.000Z",
  "title": "Generalised representations as q-connections in integral $p$-adic Hodge theory",
  "authors": [
    "Matthew Morrow",
    "Takeshi Tsuji"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over $A_{\\text{inf}}$ inspired by Faltings, modules with q-connection in the sense of q-de Rham cohomology, crystals on the prismatic site of Bhatt--Scholze, and q-deformations of Higgs bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-08T15:24:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic hodge theory",
      "q-connection",
      "q-de rham cohomology",
      "coefficient systems",
      "small generalised representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}