{
  "abstract": "Let $p$ be a prime and $k$ be an algebraic closure of the finite field with $p$ elements. Let $G$ be a connected reductive algebraic group over $k$, and let $F:G\\rightarrow G$ be a Frobenius morphism, defining an $\\mathbb{F}_q$-rational structure on $G$, where $q$ is a power of $p$. Let $\\ell$ be a prime different from $p$ and $\\ell\\ne 2$. Let $Π$ be an $\\ell$-adic cuspidal unipotent representation of $G^{F^\\ell}$ such that $Π\\simeq Π^σ$, where $σ$ is a generator the Galois group ${\\rm Gal}(\\mathbb{F}_{q^\\ell}/\\mathbb{F}_q)$. In this paper, we prove the irreducibility of the zeroth Tate cohomology group $\\widehat{\\rm H}^0(σ,\\mathcal{L})$ and vanishing of the first Tate cohomology group $\\widehat{\\rm H}^1(σ,\\mathcal{L})$ for any $G^{F^\\ell}\\rtimes{\\rm Gal}(\\mathbb{F}_{q^\\ell}/\\mathbb{F}_q)$-stable lattice $\\mathcal{L}$ in $Π$, using the multiplicity-one property of a progenerator constructed via the generalized Gelfand-Graev representations and Harish-Chandra induction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15037",
  "author_total": 1,
  "authors": [
    {
      "name": "Sabyasachi Dhar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fzfzgr725n7vp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15037",
  "fulltext_url": null,
  "id": "fzfzgr725n7vp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15037",
  "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.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221781059",
  "pdf_url": "https://arxiv.org/pdf/2610.15037",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fzfzgr725n7vp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15037"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Tate cohomology of unipotent cuspidal representations of finite groups of Lie type",
  "title_text": "Tate cohomology of unipotent cuspidal representations of finite groups of Lie type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fzfzgr725n7vp",
  "venue": "arXiv",
  "versions": []
}