{
  "abstract": "Let $f:X\\to Y$ be a morphism between smooth schemes over a perfect field $k$. Let $\\mathcal F$ be a constructible sheaf on $X$ and $Z$ a closed subscheme of $X$ such that $f$ is $SS(\\mathcal F)$-transversal outside $Z$. We construct a class supported on the non-transversal locus $Z$ by using the characteristic cycle $CC(\\mathcal F)$ defined by T. Saito. This class is a geometric counterpart of the non-acyclicity class introduced by the third author and Zhao in [Invent. Math. 240 (2025), 123-191]. Under certain conditions, the formation of this class is compatible with base change and proper pushforward. It also satisfies the Milnor formula and a conductor formula. We conjecture that the image of this geometric class under the cycle class map is the non-acyclicity class. This conjecture can be viewed as a (relative version of) Milnor-type formula for non-isolated singularities. We prove this conjecture when $k$ is algebraically closed, $X$ is quasi-affine and $Y=\\mathbb A^1_k$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25732",
  "author_total": 3,
  "authors": [
    {
      "name": "Kaicheng Bao"
    },
    {
      "name": "Jiangnan Xiong"
    },
    {
      "name": "Enlin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mj13zm3zevdy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25732",
  "fulltext_url": null,
  "id": "7mj13zm3zevdy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25732",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223035505",
  "pdf_url": "https://arxiv.org/pdf/2610.25732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mj13zm3zevdy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Characteristic cycles and non-acyclicity classes for constructible étale sheaves",
  "title_text": "Characteristic cycles and non-acyclicity classes for constructible étale sheaves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7mj13zm3zevdy",
  "venue": "arXiv",
  "versions": []
}