{
  "abstract": "Let $A$ be an abelian variety of dimension $g$ over an algebraically closed field and let $\\ell$ be a prime invertible in the field. For every constructible $\\mathbb{F}_{\\ell}$-sheaf $F$ on $A$ we prove that there is an integer $e$, depending on $F$, such that the pullback map $[\\ell^{e}]^{*}\\colon\\mathrm{H}^{i}(A,[\\ell^{n}]^{*}F)\\to\\mathrm{H}^{i}(A,[\\ell^{n+e}]^{*}F)$ is zero for all $n\\geq0$ and all $i>\\dim\\operatorname{Supp}F$. In particular $\\varinjlim\\limits_{n}\\mathrm{H}^{i}(A,[\\ell^{n}]^{*}F)=0$ for $i>\\dim\\operatorname{Supp}F$, which answers a question of Bhatt--Schnell--Scholze. Our methods also give sharp codimension estimates for the supports of the cohomology sheaves of the Fourier--Mellin transform of a perverse sheaf. With $\\ell$-adic coefficients, we remove the arithmeticity hypothesis from the estimates of Esnault--Kerz. The corresponding estimates for the completed transform with $\\mathbb{F}_{\\ell}$-coefficients are new and hold even when Hard Lefschetz fails.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35404",
  "author_total": 2,
  "authors": [
    {
      "name": "Ashutosh Roy Choudhury"
    },
    {
      "name": "K. V. Shuddhodan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4f0s2tqx7vxr9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35404",
  "fulltext_url": null,
  "id": "4f0s2tqx7vxr9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35404",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214706892",
  "pdf_url": "https://arxiv.org/pdf/2609.35404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4f0s2tqx7vxr9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Artin vanishing along the $\\ell$-adic tower of an abelian variety",
  "title_text": "Artin vanishing along the ℓ-adic tower of an abelian variety",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4f0s2tqx7vxr9",
  "venue": "arXiv",
  "versions": []
}