{
  "id": "2007.11552",
  "version": "v1",
  "published": "2020-07-22T17:15:44.000Z",
  "updated": "2020-07-22T17:15:44.000Z",
  "title": "On conjectures of Hovey--Strickland and Chai",
  "authors": [
    "Tobias Barthel",
    "Drew Heard",
    "Niko Naumann"
  ],
  "comment": "23 pages. All comments welcome",
  "categories": [
    "math.AT",
    "math.NT"
  ],
  "abstract": "We prove the height two case of a conjecture of Hovey and Strickland that provides a $K(n)$-local analogue of the Hopkins--Smith thick subcategory theorem. Our approach first reduces the general conjecture to a problem in arithmetic geometry posed by Chai. We then use the Gross--Hopkins period map to verify Chai's Hope at height two and all primes. Along the way, we show that the graded commutative ring of completed cooperations for Morava $E$-theory is coherent, and that every finitely generated Morava module can be realized by a $K(n)$-local spectrum as long as $2p-2>n^2+n$. Finally, we deduce consequences of our results for descent of Balmer spectra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-22T17:15:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "hovey-strickland",
      "hopkins-smith thick subcategory theorem",
      "approach first reduces",
      "gross-hopkins period map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}