{
  "abstract": "For a constructible sheaf $\\mathcal{F}$ on a smooth scheme $X$ over a perfect field, the singular support $SS(\\mathcal{F})$ and the characteristic cycle $CC(\\mathcal{F})$ are defined on the cotangent bundle. In analogy with the construction of Kashiwara--Schapira via microlocalization in the transcendental setting, we construct the microlocal versions ${ SS}_μ(\\mathcal{F})$ and $CC_μ(\\mathcal{F})$ of $SS(\\mathcal{F})$ and $CC(\\mathcal{F})$ respectively, and prove \\[ SS_μ(\\mathcal{F})= SS(\\mathcal{F}),\\qquad CC_μ(\\mathcal{F})= {\\rm cl}CC(\\mathcal{F}), \\] where $\\operatorname{cl}$ is the cycle class map. As a consequence of the second equality, we show that the cohomological characteristic classes are the cycle classes associated with the corresponding characteristic cycles, as conjectured in (\\emph{Invent.~Math.~207: 597--695, 2017}). As further applications, we give new proofs of the index formula and Bloch's conductor formula in the proper case, independently of Abe's homotopical approach via $\\infty$-categories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06625",
  "author_total": 3,
  "authors": [
    {
      "name": "Takeshi Saito"
    },
    {
      "name": "Jiangnan Xiong"
    },
    {
      "name": "Enlin Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vgqbc575bzy2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06625",
  "fulltext_url": null,
  "id": "4vgqbc575bzy2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06625",
  "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": "W7212002005",
  "pdf_url": "https://arxiv.org/pdf/2609.06625",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vgqbc575bzy2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2609.06625",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06625"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Singular supports, characteristic cycles, and microlocalization of constructible sheaves",
  "title_text": "Singular supports, characteristic cycles, and microlocalization of constructible sheaves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/4vgqbc575bzy2",
  "venue": "arXiv",
  "versions": []
}