On Chow weight structures for cdh-motives with integral coefficients

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On Chow weight structures for cdh-motives with integral coefficients. / Bondarko, M. V.; Ivanov, M. A.

In: St. Petersburg Mathematical Journal, Vol. 27, No. 6, 01.01.2016, p. 869-888.

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Author

Bondarko, M. V. ; Ivanov, M. A. / On Chow weight structures for cdh-motives with integral coefficients. In: St. Petersburg Mathematical Journal. 2016 ; Vol. 27, No. 6. pp. 869-888.

BibTeX

@article{0b776f1fe32e455a84cdae1decb5ed19,

title = "On Chow weight structures for cdh-motives with integral coefficients",

abstract = "The paper is aimed at defining a certain Chow weight structure wChow on the category DMc(S) of (constructible) cdh-motives over an equicharacteristic scheme S. In contrast to the previous papers of D. H{\'e}bert and the first author on weights for relative motives (with rational coefficients), this goal is achieved for motives with integral coefficients (if char S = 0; if char S = p > 0, then motives with ℤ[1/p]-coefficients are considered). It is proved that the properties of the Chow weight structures that were previously established for Q-linear motives can be carried over to this {"}integral{"} context (and some of them are generalized using certain new methods). Mostly, the version of wChow defined via {"}gluing from strata{"} is studied; this makes it possible to define Chow weight structures for a wide class of base schemes. As a consequence, certain (Chow)-weight spectral sequences and filtrations are obtained on any (co)homology of motives.",

keywords = "Cdh-topology, Deligne's weights, Triangulated categories, Voevodsky motives, Weight structures",

author = "Bondarko, {M. V.} and Ivanov, {M. A.}",

year = "2016",

month = jan,

day = "1",

doi = "10.1090/spmj/1424",

language = "English",

volume = "27",

pages = "869--888",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "6",

}

RIS

TY - JOUR

T1 - On Chow weight structures for cdh-motives with integral coefficients

AU - Bondarko, M. V.

AU - Ivanov, M. A.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - The paper is aimed at defining a certain Chow weight structure wChow on the category DMc(S) of (constructible) cdh-motives over an equicharacteristic scheme S. In contrast to the previous papers of D. Hébert and the first author on weights for relative motives (with rational coefficients), this goal is achieved for motives with integral coefficients (if char S = 0; if char S = p > 0, then motives with ℤ[1/p]-coefficients are considered). It is proved that the properties of the Chow weight structures that were previously established for Q-linear motives can be carried over to this "integral" context (and some of them are generalized using certain new methods). Mostly, the version of wChow defined via "gluing from strata" is studied; this makes it possible to define Chow weight structures for a wide class of base schemes. As a consequence, certain (Chow)-weight spectral sequences and filtrations are obtained on any (co)homology of motives.

AB - The paper is aimed at defining a certain Chow weight structure wChow on the category DMc(S) of (constructible) cdh-motives over an equicharacteristic scheme S. In contrast to the previous papers of D. Hébert and the first author on weights for relative motives (with rational coefficients), this goal is achieved for motives with integral coefficients (if char S = 0; if char S = p > 0, then motives with ℤ[1/p]-coefficients are considered). It is proved that the properties of the Chow weight structures that were previously established for Q-linear motives can be carried over to this "integral" context (and some of them are generalized using certain new methods). Mostly, the version of wChow defined via "gluing from strata" is studied; this makes it possible to define Chow weight structures for a wide class of base schemes. As a consequence, certain (Chow)-weight spectral sequences and filtrations are obtained on any (co)homology of motives.

KW - Cdh-topology

KW - Deligne's weights

KW - Triangulated categories

KW - Voevodsky motives

KW - Weight structures

UR - http://www.scopus.com/inward/record.url?scp=84999114791&partnerID=8YFLogxK

U2 - 10.1090/spmj/1424

DO - 10.1090/spmj/1424

M3 - Article

AN - SCOPUS:84999114791

VL - 27

SP - 869

EP - 888

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 6

ER -

ID: 62103178