{
  "id": "1002.2651",
  "version": "v6",
  "published": "2010-02-15T18:47:49.000Z",
  "updated": "2011-05-02T19:04:45.000Z",
  "title": "Z[1/p]-motivic resolution of singularities",
  "authors": [
    "Mikhail V. Bondarko"
  ],
  "comment": "Some minor corrections made; to appear in Compositio Mathematica",
  "journal": "Compos. Math. 147 (2011), no. 5, 1434-1446",
  "doi": "10.1112/S0010437X11005410",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "The main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with $Z[1/p]$-coefficients over a perfect field $k$ of characteristic $p$ generate the category $DM^{eff}_{gm}[1/p]$ (of effective geometric Voevodsky's motives with $Z[1/p]$-coefficients). It follows that $DM^{eff}_{gm}[1/p]$ could be endowed with a Chow weight structure $w_{Chow}$ whose heart is $Chow^{eff}[1/p]$ (weight structures were introduced in a preceding paper, where the existence of $w_{Chow}$ for $DM^{eff}_{gm}Q$ was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor $DM^{eff}_{gm}[1/p]\\to K^b(Chow^{eff}[1/p])$ (which induces an isomorphism on $K_0$-groups), as well as the existence of canonical and functorial (Chow)-weight spectral sequences and weight filtrations for any cohomology theory on $DM^{eff}_{gm}[1/p]$. We also define a certain Chow t-structure for $DM_{-}^{eff}[1/p]$ and relate it with unramified cohomology. To this end we study birational motives and birational homotopy invariant sheaves with transfers.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-05-02T19:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S45",
      "14C15",
      "14E15",
      "14F42",
      "14G17",
      "19E15",
      "14C25",
      "14F20",
      "18E40",
      "18E30",
      "13D15",
      "18G40",
      "19A99"
    ],
    "keywords": [
      "resolution",
      "birational homotopy invariant sheaves",
      "chow weight structure",
      "conservative weight complex functor",
      "study birational motives"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.2651B"
    }
  }
}