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

In: АЛГЕБРА И АНАЛИЗ, Vol. 27, No. 6, 2015, p. 14-40.

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Harvard

Bondarko, MV & Ivanov, MA 2015, 'On Chow weight structures for cdh-motives with integral coefficients', АЛГЕБРА И АНАЛИЗ, vol. 27, no. 6, pp. 14-40.

APA

Bondarko, M. V., & Ivanov, M. A. (2015). On Chow weight structures for cdh-motives with integral coefficients. АЛГЕБРА И АНАЛИЗ, 27(6), 14-40.

Vancouver

Bondarko MV, Ivanov MA. On Chow weight structures for cdh-motives with integral coefficients. АЛГЕБРА И АНАЛИЗ. 2015;27(6):14-40.

Author

Bondarko, M.V. ; Ivanov, M.A. / On Chow weight structures for cdh-motives with integral coefficients. In: АЛГЕБРА И АНАЛИЗ. 2015 ; Vol. 27, No. 6. pp. 14-40.

BibTeX

@article{ffc3b564d0364185ac597191b3cf7201,
title = "On Chow weight structures for cdh-motives with integral coefficients",
abstract = "Our main goal in this paper is to define 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), we can achieve our goal for motives with integral coefficients (if charS=0; if charS=p>0, then we consider motives with Z[1p]-coefficients). We prove 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 we generalize some of them using certain new methods). In this paper we mostly study the version of wChow defined via “gluing from strata”; this enables us to define Chow weight structures for a wide class of base schemes. As a consequence, we certainly obtain certain (Chow)-weight spectral sequences and filtrations on any (co)homology of motives.",
keywords = "Voevodsky motives, Triangulated categories, Weight structures, Deligne's weights, cdh-topology",
author = "M.V. Bondarko and M.A. Ivanov",
note = "M. V. Bondarko, M. A. Ivanov, “On Chow weight structures for cdh-motives with integral coefficients”, Алгебра и анализ, 27:6 (2015), 14–40; St. Petersburg Math. J., 27:6 (2016), 869–888",
year = "2015",
language = "English",
volume = "27",
pages = "14--40",
journal = "АЛГЕБРА И АНАЛИЗ",
issn = "0234-0852",
publisher = "Издательство {"}Наука{"}",
number = "6",

}

RIS

TY - JOUR

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

AU - Bondarko, M.V.

AU - Ivanov, M.A.

N1 - M. V. Bondarko, M. A. Ivanov, “On Chow weight structures for cdh-motives with integral coefficients”, Алгебра и анализ, 27:6 (2015), 14–40; St. Petersburg Math. J., 27:6 (2016), 869–888

PY - 2015

Y1 - 2015

N2 - Our main goal in this paper is to define 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), we can achieve our goal for motives with integral coefficients (if charS=0; if charS=p>0, then we consider motives with Z[1p]-coefficients). We prove 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 we generalize some of them using certain new methods). In this paper we mostly study the version of wChow defined via “gluing from strata”; this enables us to define Chow weight structures for a wide class of base schemes. As a consequence, we certainly obtain certain (Chow)-weight spectral sequences and filtrations on any (co)homology of motives.

AB - Our main goal in this paper is to define 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), we can achieve our goal for motives with integral coefficients (if charS=0; if charS=p>0, then we consider motives with Z[1p]-coefficients). We prove 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 we generalize some of them using certain new methods). In this paper we mostly study the version of wChow defined via “gluing from strata”; this enables us to define Chow weight structures for a wide class of base schemes. As a consequence, we certainly obtain certain (Chow)-weight spectral sequences and filtrations on any (co)homology of motives.

KW - Voevodsky motives

KW - Triangulated categories

KW - Weight structures

KW - Deligne's weights

KW - cdh-topology

UR - http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=aa&paperid=1465&option_lang=rus

M3 - Article

VL - 27

SP - 14

EP - 40

JO - АЛГЕБРА И АНАЛИЗ

JF - АЛГЕБРА И АНАЛИЗ

SN - 0234-0852

IS - 6

ER -

ID: 5792908