{
  "abstract": "Using methods similar to Morel's stable connectivity theorem, we prove that, over an arbitrary field, the Tate truncation functors $f_{0/n}$ preserve motivic connectivity of $ S^1$-spectra. An analogous result for complexes yields a Hurewicz theorem for the $L^{p,n}$- and $L_{bir}^n$-localizations over perfect fields. Over such fields, we establish a stronger connectivity property for categories of correspondences, showing that $f_n^\\mathcal{C}$ preserves connectivity of motivic spectra with $\\mathcal{C}$-transfers, whenever $\\mathcal{C}$ satisfies cancellation. We then use the motivic reconstruction theorem to deduce that $f_n$, and consequently $s_n$ and $f_{0/n}$, also preserve connectivity for effective (and thereby, $\\mathbb{P}^1$-) motivic spectra. Along the way, we also establish the slice analog of the motivic (effective) reconstruction theorem, as well as the slice analog of motivic $S^1$- and $\\mathbb{P}^1$-recognition theorems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34535",
  "author_total": 1,
  "authors": [
    {
      "name": "Dipankar Maity"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e54qwkexdkhw9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34535",
  "fulltext_url": null,
  "id": "e54qwkexdkhw9",
  "issns": [],
  "landing_url": "https://hal.science/hal-05768406v1",
  "language": "en",
  "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"
    ],
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      "hal",
      "0.math"
    ],
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      "hal",
      "1.math.math-ag"
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7214737774",
  "pdf_url": "https://arxiv.org/pdf/2609.34535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e54qwkexdkhw9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:42Z",
      "native_id": "hal-05768406",
      "source": "hal",
      "url": "https://hal.science/hal-05768406v1"
    },
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Connectivity of the slice filtration",
  "title_text": "Connectivity of the slice filtration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/e54qwkexdkhw9",
  "venue": "HAL",
  "versions": []
}