{
  "id": "2011.12106",
  "version": "v1",
  "published": "2020-11-24T14:23:57.000Z",
  "updated": "2020-11-24T14:23:57.000Z",
  "title": "Flat replacements of homology theories",
  "authors": [
    "Daniel Schäppi"
  ],
  "comment": "45 pages",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "To a homology theory one can associate an additive site and a new homological functor with values in the category of additive sheaves on that site. If this category of sheaves can be shown to be equivalent to a category of comodules of a Hopf algebroid, then we obtain a new homology theory by composing with the underlying module functor. This new homology theory is always flat and we call it a flat replacement of the original theory. For example, Pstr\\k{a}gowski has shown that complex cobordism is a flat replacement of singular homology. In this article we study the basic properties of the sites associated to homology theories and we prove an existence theorem for flat replacements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-24T14:23:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N20",
      "18G80",
      "18M05"
    ],
    "keywords": [
      "homology theory",
      "flat replacement",
      "complex cobordism",
      "existence theorem",
      "original theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}