{
  "id": "1808.00895",
  "version": "v1",
  "published": "2018-08-01T09:01:11.000Z",
  "updated": "2018-08-01T09:01:11.000Z",
  "title": "Derived completion for comodules",
  "authors": [
    "Tobias Barthel",
    "Drew Heard",
    "Gabriel Valenzuela"
  ],
  "comment": "All comments are welcome. arXiv admin note: text overlap with arXiv:1511.03526",
  "categories": [
    "math.AT",
    "math.AC"
  ],
  "abstract": "The objective of this paper is to study completions and the local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to comodule-theoretic completion, construct various local homology spectral sequences, and derive a tilting-theoretic interpretation of local duality for modules. Our results translate to quasi-coherent sheaves over global quotient stacks and feed into a novel approach to the chromatic splitting conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-01T09:01:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P60",
      "13D45",
      "14B15",
      "55U35"
    ],
    "keywords": [
      "derived completion",
      "local homology spectral sequences",
      "global quotient stacks",
      "comodule-theoretic completion",
      "chromatic splitting conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}