{
  "id": "2012.06098",
  "version": "v2",
  "published": "2020-12-11T03:37:52.000Z",
  "updated": "2022-03-22T13:42:46.000Z",
  "title": "Co-$t$-structures on derived categories of coherent sheaves and the cohomology of tilting modules",
  "authors": [
    "Pramod N. Achar",
    "William Hardesty"
  ],
  "comment": "40 pages. v2: extensive corrections; added details in some proofs",
  "categories": [
    "math.RT",
    "math.CT",
    "math.GR"
  ],
  "abstract": "We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\\mathcal{N}$ of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These structures are employed to show that the push-forwards of the \"exotic parity objects\" along the (classical) Springer resolution give indecomposable objects inside the coheart of the co-$t$-structure on $\\mathcal{N}$. We also demonstrate how the various parabolic co-$t$-structures can be related by introducing an analogue to the usual translation functors. As an application, we give a proof of a scheme-theoretic formulation of the relative Humphreys conjecture on support varieties of tilting modules in type $A$ for $p>h$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-22T13:42:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coherent sheaves",
      "derived category",
      "tilting modules",
      "cohomology",
      "parabolic springer resolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}