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Algebra i Analiz, 2015, Volume 27, Issue 6, Pages 14–40 (Mi aa1465)  

This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

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

M. V. Bondarko, M. A. Ivanov

Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ pr., 28, Petergof, 198504, St. Petersburg, Russia

Abstract: Our main goal in this paper is to define a certain Chow weight structure $w_\mathrm{Chow}$ on the category $\mathcal{DM}_c(S)$ 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 $\operatorname{char}S=0$; if $\operatorname{char}S=p>0$, then we consider motives with $\mathbb Z[\frac1p]$-coefficients). We prove that the properties of the Chow weight structures that were previously established for $\mathbb Q$-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 $w_\mathrm{Chow}$ 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00393A
15-01-03034A
Dynasty Foundation
Supported by RFBR (grants no. 14-01-00393A and 15-01-03034A). The first author is also grateful to Dmitry Zimin's Foundation “Dynasty”.


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English version:
St. Petersburg Mathematical Journal, 2016, 27:6, 869–888

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Received: 12.04.2015
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Citation: M. V. Bondarko, M. A. Ivanov, “On Chow weight structures for $cdh$-motives with integral coefficients”, Algebra i Analiz, 27:6 (2015), 14–40; St. Petersburg Math. J., 27:6 (2016), 869–888

Citation in format AMSBIB
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\by M.~V.~Bondarko, M.~A.~Ivanov
\paper On Chow weight structures for $cdh$-motives with integral coefficients
\jour Algebra i Analiz
\yr 2015
\vol 27
\issue 6
\pages 14--40
\mathnet{http://mi.mathnet.ru/aa1465}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3589220}
\elib{http://elibrary.ru/item.asp?id=26414156}
\transl
\jour St. Petersburg Math. J.
\yr 2016
\vol 27
\issue 6
\pages 869--888
\crossref{https://doi.org/10.1090/spmj/1424}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84999114791}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Bondarko, V. A. Sosnilo, “On the weight lifting property for localizations of triangulated categories”, Lobachevskii J. Math., 39:7 (2018), 970–984  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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