{
  "abstract": "Applying the BBDJS minimal model to the derived symplectification of a $-1$-shifted contact derived Artin stack and descending algebraically along the structural free $\\mathbb{G}_m$-action, we construct an $\\ell$-adic perverse sheaf on any oriented such stack, and use Verdier's specialization equivalence for monodromic sheaves to equip it with a tame twisted monodromy operator $θ$. We show that the local fundamental class of a Legendrian $L$ satisfies $θ\\circ μ_L = (-1)^{\\mathrm{vdim} L}μ_L$, so that on Legendrians of odd virtual dimension, the class vanishes due to $θ$-invariance. Moreover, both parities occur already on the $A_1$ chart while an odd Legendrian can carry a nonzero local class. We further formulate a contact analogue of Joyce's conjecture for a graded orientation, in which the orientation datum is twisted by the parity of the virtual dimension. Under the assumption of a monodromic refinement of the symplectic conjecture, we construct the categorified Legendrian 2-categories $\\mathfrak{L}\\mathcal{F}_c(X)$ and $LLeg_0$ via $\\ell$-adic pull-push functors. Finally, we show that the contact Behrend function is identically $1$, so that the associated Donaldson-Thomas invariant is the compactly supported étale Euler characteristic of the classical truncation, and that the higher traces of $θ$ recover the singularity type that the first trace discards. As an application, we show that the symplectic invariant of a derived intersection of conic Lagrangians in a cotangent bundle vanishes identically, while the contact invariant computes the Euler characteristic of the projectivized intersection, with an explicit formula for conormal bundles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18796",
  "author_total": 1,
  "authors": [
    {
      "name": "Efe İzbudak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mpka9vqfvjcw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18796",
  "fulltext_url": null,
  "id": "4mpka9vqfvjcw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18796",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213494704",
  "pdf_url": "https://arxiv.org/pdf/2609.18796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mpka9vqfvjcw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Monodromic Perverse Sheaves on Shifted Contact Stacks",
  "title_text": "Monodromic Perverse Sheaves on Shifted Contact Stacks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/4mpka9vqfvjcw",
  "venue": "arXiv",
  "versions": []
}