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ℤ[1/p]-motivic resolution of singularities

Part of: Abelian categories Birational geometry Cycles and subschemes (Co)homology theory Arithmetic problems. Diophantine geometry $K$-theory in geometry Commutative algebra: Homological methods

Published online by Cambridge University Press:  01 June 2011

M. V. Bondarko
M. V. Bondarko*
Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya Pl. 2, 198904, St. Petersburg, Russia (email: [email protected])
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Abstract

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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 DMeffgm[1/p] (of effective geometric Voevodsky’s motives with ℤ[1/p]-coefficients). It follows that DMeffgm[1/p] 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 DMeffgmℚ was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor DMeffgm[1/p]→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 DMeffgm[1/p] . We also mention a certain Chow t-structure for DMeff−[1/p] and relate it with unramified cohomology.

Keywords

motivestriangulated categoriescohomologyweight structuresresolution of singularitiesalterations

MSC classification

Secondary: 14E15: Global theory and resolution of singularities 14G17: Positive characteristic ground fields 14C15: (Equivariant) Chow groups and rings; motives 18E30: Derived categories, triangulated categories 18E40: Torsion theories, radicals 19E15: Algebraic cycles and motivic cohomology 14F42: Motivic cohomology; motivic homotopy theory 14F20: Étale and other Grothendieck topologies and (co)homologies 13D15: Grothendieck groups, $K$-theory 14C25: Algebraic cycles
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 5 , September 2011 , pp. 1434 - 1446
Copyright
Copyright © Foundation Compositio Mathematica 2011

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