## 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 [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 w_{Chow} whose heart is Chow^{eff}[1/p] (weight structures were introduced in a preceding paper, where the existence of w_{Chow} 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]→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 [formula omitted]. We also mention a certain Chow t-structure for [formula omitted] and relate it with unramified cohomology.

Original language | English |
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Pages (from-to) | 1434-1446 |

Number of pages | 13 |

Journal | Compositio Mathematica |

Volume | 147 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 2011 |

## Scopus subject areas

- Algebra and Number Theory

## Keywords

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