{
  "abstract": "At every prime $p$, we disprove the algebraic generating hypothesis for compact objects in Hovey's stable category of $BP_*BP$-comodules and its local analog at every positive height, answering questions of Barthel and Heard. In both settings, for every $r,n\\geq1$, we construct a ghost whose first $n$ composition powers are all nonzero and have exact additive order $p^r$. The same construction applies to the stable category of $E_*E$-comodules for even $p$-local Landweber exact theories $E$ that are not rational. Through the motivic deformation of Gheorghe--Wang--Xu, these examples give $Cτ$-linear counterexamples to the cellular $\\mathbb{C}$-motivic generating hypothesis, with the same order and composition properties. We also construct nonzero non-$Cτ$-linear ghosts between $Cτ$-modules and a nonzero ghost on a motivic spectrum with noncontractible Betti realization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15253",
  "author_total": 2,
  "authors": [
    {
      "name": "Sihao Ma"
    },
    {
      "name": "Zhouli Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cc343qj49zx96.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15253",
  "fulltext_url": null,
  "id": "cc343qj49zx96",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15253",
  "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.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7213360749",
  "pdf_url": "https://arxiv.org/pdf/2609.15253",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cc343qj49zx96.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.15253",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15253"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generating hypotheses along the motivic deformation",
  "title_text": "Generating hypotheses along the motivic deformation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/cc343qj49zx96",
  "venue": "arXiv",
  "versions": []
}