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ℤ[1/p]-motivic resolution of singularities. / Bondarko, M. V.
в: Compositio Mathematica, Том 147, № 5, 01.01.2011, стр. 1434-1446.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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