{
  "abstract": "We develop a purely algebraic framework for index-type theorems based on the Rees construction for filtered differential graded algebras (FDGAs). Alongside the classical Rees module we introduce a smooth variant $C^ω_{\\mathcal{R}}A$, adapted to analytic arguments, and we study traces and their pointwise and coefficient-wise extensions to Rees algebras. The main result (Corollary 3.11) is an abstract index theorem: given a compatible datum of filtered differential graded associative algebras with traces $A$, $B$, $G$ with a morphism $ϕ\\colon A\\to B$, an action $ρ\\colon G\\otimes A\\to A$ and a morphism $i\\colon G\\to B$, together with a graded-central element, one has $\\mathrm{tr}_B(e^{f_0+f_1}) = \\mathrm{tr}_{\\widehat{\\mathrm{gr}}A}(e^γh)$, where the left-hand side is the trace in $B$ and the right-hand side the trace in the Laurent series associated graded $\\widehat{\\mathrm{gr}}A$ of $A$. Here $f_0+f_1$ is a curvature-type element, i.e., an element of the form $d_Bβ+β^2$ for some odd-degree element $β$, while $γ$ and $h$ are certain elements in $\\widehat{\\mathrm{gr}}A$. The formalism is modelled on the Getzler rescaling technique and on the derivation of the localization formula for the loop space Chern character by Ludewig and Yi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30587",
  "author_total": 1,
  "authors": [
    {
      "name": "Eugenio Landi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4840bjb8y012t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30587",
  "fulltext_url": null,
  "id": "4840bjb8y012t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30587",
  "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.DG"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7204965994",
  "pdf_url": "https://arxiv.org/pdf/2608.30587",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4840bjb8y012t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30587",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30587"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An Abstract Index Theorem via Rees Algebras",
  "title_text": "An Abstract Index Theorem via Rees Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/4840bjb8y012t",
  "venue": "arXiv",
  "versions": []
}