{
  "abstract": "We compute top derived products and inverse limits on products of affine lines with doubled origin over $B[s]$, for any nonzero commutative ring $B$. For every $B$-module $M$, the two top obstruction modules fit into an explicit exact sequence and contain $M^{\\mathbb N}/M^{(\\mathbb N)}$as a natural $B$-module direct summand.This gives exact product dimensions, sharp vanishing bounds for inverse sequences, and faithfulness in the coefficient module. For a Grothendieck category of finite product dimension, we also obtain degree shifts under adjoining commuting locally nilpotent endomorphisms and prove that this construction preserves top-degree vanishing for epimorphic inverse sequences. A fixed Gabriel--Popescu presentation then describes the general top obstruction through actual Ext sequences and separates two module-theoretic terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41117",
  "author_total": 2,
  "authors": [
    {
      "name": "Rui Zeng"
    },
    {
      "name": "Guocheng Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkepv96g1ffhp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41117",
  "fulltext_url": null,
  "id": "fkepv96g1ffhp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41117",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkepv96g1ffhp.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Derived products and top-degree inverse limits",
  "title_text": "Derived products and top-degree inverse limits",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/fkepv96g1ffhp",
  "venue": "arXiv",
  "versions": []
}