{
  "abstract": "Let $R$ be a commutative noetherian ring. We ask whether complexes with finitely generated cohomology and a fixed support can be generated by relatively compact objects, using coproducts which exist in the half-bounded derived category. We prove that $\\mathbf D^+_{\\mathrm{fg},W}(R)=\\operatorname{Loc}_{\\mathrm{ex}}(\\mathbf D^b_{\\mathrm{fg},W}(R))$ whenever $W\\subseteq\\operatorname{Spec} R$ is specialization closed and has finite dimension. The same equality holds for every specialization-closed subset of $\\operatorname{Spec} B$ when $B$ is a finite-type algebra over a noetherian domain $A$ of finite character and either $A$ or $B$ is regular. These equalities classify the thick Hom-submodules closed under existing coproducts. We also prove the corresponding bounded-above statement from the support results of Matsui--Takahashi. For an arbitrary noetherian ring, the bounded-below generation conjecture reduces to torsion complexes over quotient domains, with their support unchanged. Finally, over a regular noetherian domain of infinite dimension, we give a bounded-below object which is generated by bounded objects with the same support but has no bounded-below representative by finitely generated modules. The comparison functor from the bounded-below derived category of finite modules is therefore neither full nor essentially surjective.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04690",
  "author_total": 1,
  "authors": [
    {
      "name": "Liangyu Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hf6e5aat0xxx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04690",
  "fulltext_url": null,
  "id": "6hf6e5aat0xxx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04690",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04690",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hf6e5aat0xxx.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04690",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04690"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Relative Telescope-Type Conjecture: Support and Generation in Half-Bounded Derived Categories",
  "title_text": "A Relative Telescope-Type Conjecture: Support and Generation in Half-Bounded Derived Categories",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/6hf6e5aat0xxx",
  "venue": "arXiv",
  "versions": []
}