On Chow weight structures without projectivity and resolution of singularities

Mikhail V. Bondarko, David Z. Kumallagov

Published 2017-11-22Version 1

In this paper certain Chow weight structures on the "big" triangulated motivic categories $DM_R^{eff}\subset DM_R$ 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 the weight structures that were 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.