ℤ[1/p]-motivic resolution of singularities

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23 Scopus citations


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 [formula omitted] (of effective geometric Voevodsky’s motives with ℤ[1/p]-coefficients). It follows that [formula omitted] can be endowed with a Chow weight structure wChow whose heart is Choweff[1/p] (weight structures were introduced in a preceding paper, where the existence of wChow for [formula omitted] was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor [formula omitted]→Kb (Choweff [1/p]) (which induces an isomorphism on K0-groups), as well as the existence of canonical and functorial (Chow)-weight spectral sequences and weight filtrations for any cohomology theory on [formula omitted]. We also mention a certain Chow t-structure for [formula omitted] and relate it with unramified cohomology.

Original languageEnglish
Pages (from-to)1434-1446
Number of pages13
JournalCompositio Mathematica
Issue number5
StatePublished - 1 Jan 2011

Scopus subject areas

  • Algebra and Number Theory


  • alterations
  • cohomology
  • motives
  • resolution of singularities
  • triangulated categories
  • weight structures


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