TY - JOUR

T1 - On Chow weight structures without projectivity and resolution of singularities

AU - Bondarko, M. V.

AU - Kumallagov, D. Z.

PY - 2019/10

Y1 - 2019/10

N2 - In this paper certain Chow weight structures on the "big" triangulated motivic categories DMeff R ⊂ DMR are defined in terms of motives of all smooth varieties over the ground field. This definition allows the study of basic properties of these weight structures without applying resolution of singularities; thus, it is possible to lift the assumption that the coefficient ring R contains 1/p in the case where the characteristic p of the ground field is positive. Moreover, in the case where R does satisfy the last assumption, our weight structures are "compatible" with the weight structures that were defined in previous papers in terms of Chow motives; it follows that a motivic complex has nonnegative weights if and only if its positive Nisnevich hypercohomology vanishes. The results of this article yield certain Chow-weight filtration (also) on p-adic cohomology of motives and smooth varieties.

AB - In this paper certain Chow weight structures on the "big" triangulated motivic categories DMeff R ⊂ DMR are defined in terms of motives of all smooth varieties over the ground field. This definition allows the study of basic properties of these weight structures without applying resolution of singularities; thus, it is possible to lift the assumption that the coefficient ring R contains 1/p in the case where the characteristic p of the ground field is positive. Moreover, in the case where R does satisfy the last assumption, our weight structures are "compatible" with the weight structures that were defined in previous papers in terms of Chow motives; it follows that a motivic complex has nonnegative weights if and only if its positive Nisnevich hypercohomology vanishes. The results of this article yield certain Chow-weight filtration (also) on p-adic cohomology of motives and smooth varieties.

KW - Compact objects

KW - Deligne weights

KW - T-structures

KW - Triangulated categories

KW - Voevodsky and Chow motives

KW - Weight structures

UR - http://www.scopus.com/inward/record.url?scp=85070559777&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=41623701

UR - https://www.ams.org/journals/spmj/2019-30-05/home.html

U2 - 10.1090/spmj/1570

DO - 10.1090/spmj/1570

M3 - Article

AN - SCOPUS:85070559777

VL - 30

SP - 803

EP - 819

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -