{
  "annotation_id": "bcd56f6a-fca1-44bd-a47f-43581339182d",
  "date_created": "2026-02-17T05:53:20.331000Z",
  "date_modified": "2026-02-17T05:53:20.331000Z",
  "file_hash": "94d7e810edcb81c59427074c27d4b179efcfde9960759a70ca89123a935bc542",
  "private": false,
  "record": {
    "abstract": "The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable functors: it is shown that, for any ring, the pure global dimension of the derived category is at least the pure global dimension of the ring; expanding results of Beligiannis and Keller-Christensen-Neeman. This result is obtained by constructing `change of category\u0027 isomorphisms of PExt groups across definable functors. The same isomorphisms illustrate circumstances when one can transfer the property of Brown--Adams representability. We demonstrate how these methods can be used to test whether certain derived category of quasi-coherent sheaves are a Brown category. We also make an investigation into the structure of derived categories of von Neumann regular rings, which are shown in many cases to control Brown--Adams representability; this includes a new proof of the telescope conjecture, and a new and short proof that a coherent ring satisfies Freyd\u0027s (strong) generating hypothesis if and only if it is von Neumann regular.",
    "arxiv_id": "2601.09443",
    "authors": [
      "Isaac Bird"
    ],
    "categories": [
      "math.RT",
      "math.AT",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Definable functors and Brown--Adams representability",
    "url": "https://arxiv.org/abs/2601.09443",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "31687ca4-c5ce-46c7-a4c4-c47fbd7a4e0f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}