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ℤ[1/p]-motivic resolution of singularities. / Bondarko, M. V.

In: Compositio Mathematica, Vol. 147, No. 5, 01.01.2011, p. 1434-1446.

Research output: Contribution to journal › Article › peer-review

Harvard

Bondarko, MV 2011, 'ℤ[1/p]-motivic resolution of singularities', Compositio Mathematica, vol. 147, no. 5, pp. 1434-1446. https://doi.org/10.1112/S0010437X11005410

APA

Bondarko, M. V. (2011). ℤ[1/p]-motivic resolution of singularities. Compositio Mathematica, 147(5), 1434-1446. https://doi.org/10.1112/S0010437X11005410

Vancouver

Bondarko MV. ℤ[1/p]-motivic resolution of singularities. Compositio Mathematica. 2011 Jan 1;147(5):1434-1446. https://doi.org/10.1112/S0010437X11005410

Author

Bondarko, M. V. / ℤ[1/p]-motivic resolution of singularities. In: Compositio Mathematica. 2011 ; Vol. 147, No. 5. pp. 1434-1446.

BibTeX

@article{8a8a01d5de464ed09d5b0cb72d2ca7fa,
title = "ℤ[1/p]-motivic resolution of singularities",
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{\textquoteright}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.",
keywords = "alterations, cohomology, motives, resolution of singularities, triangulated categories, weight structures",
author = "Bondarko, {M. V.}",
year = "2011",
month = jan,
day = "1",
doi = "10.1112/S0010437X11005410",
language = "English",
volume = "147",
pages = "1434--1446",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "5",

}

RIS

TY - JOUR

T1 - ℤ[1/p]-motivic resolution of singularities

AU - Bondarko, M. V.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - alterations

KW - cohomology

KW - motives

KW - resolution of singularities

KW - triangulated categories

KW - weight structures

UR - http://www.scopus.com/inward/record.url?scp=84865413605&partnerID=8YFLogxK

U2 - 10.1112/S0010437X11005410

DO - 10.1112/S0010437X11005410

M3 - Article

AN - SCOPUS:84865413605

VL - 147

SP - 1434

EP - 1446

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 0010-437X

IS - 5

ER -

ID: 35957735