{
  "abstract": "Let $f: X\\rightarrow S$ be a faithful affine map. In this article we construct a group homomorphism $θ_{fppf}: \\text{Br}(f) \\longrightarrow H^1_{fppf}\\!\\left(S, (f_*\\mathcal{O}_X^\\times / \\mathcal{O}_S^\\times)_{fppf}\\right)$, extending the formerly defined morphism over an étale site $θ_{et}$. In doing so, we eliminate the characteristic constraint previously found in the relative version of Kummer's exact sequence. Furthermore, given a finite subintegral extension of noetherian rings $A \\hookrightarrow B$, we show that all the $fppf$ cohomology groups, $H^i_{fppf}(Spec(A),μ^f_n); \\;\\forall i\\geq 0$ vanish whenever $n$ does not divide the characteristic of $A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04760",
  "author_total": 1,
  "authors": [
    {
      "name": "Sourayan Banerjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8h032r2s3pm58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04760",
  "fulltext_url": null,
  "id": "8h032r2s3pm58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04760",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7211896305",
  "pdf_url": "https://arxiv.org/pdf/2609.04760",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8h032r2s3pm58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.04760",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04760"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Relative Brauer groups and Kummer Sequence without characteristic constraint in $fppf$-topology",
  "title_text": "Relative Brauer groups and Kummer Sequence without characteristic constraint in fppf-topology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8h032r2s3pm58",
  "venue": "arXiv",
  "versions": []
}