On Chow weight structures without projectivity and resolution of singularities

2017/11/22 by Bondarko, Mikhail V., Kumallagov, David Z.
#14C15 #14F05 #14F20 #14F42 #18E30 #18E35 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1711.08454

Abstract

In this paper certain Chow weight structures on the "big" triangulated motivic categories DM_R^eff⊂ DM_R are defined in terms of motives of all smooth varieties over the base field. This definition allows studying basic properties of these weight structures without applying resolution of singularities; thus we don't have to assume that the coefficient ring R contains 1/p in the case where the characteristic p of the base field is positive. Moreover, in the case where R satisfies the latter assumption our weight structures are "compatible" with Chow weight structures defined in previous papers (in terms of Chow motives). The results of this article yield certain Chow-weight filtration (also) on p-adic cohomology of motives and smooth varieties.

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