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

Authors:
M. V. Bondarko and M. A. Ivanov

Original publication:
Algebra i Analiz, tom **27** (2015), nomer 6.

Journal:
St. Petersburg Math. J. **27** (2016), 869-888

MSC (2010):
Primary 14C15; Secondary 19E15, 14C25, 14F20, 14E18, 18E30, 13D15, 18E40

DOI:
https://doi.org/10.1090/spmj/1424

Published electronically:
September 30, 2016

MathSciNet review:
3589220

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

The paper is aimed at defining 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), this goal is achieved for motives with integral coefficients (if $\mathrm {char}\thinspace S=0$; if $\mathrm {char}\thinspace S=p>0$, then motives with ${\mathbb {Z}}[\frac {1}{p}]$-coefficients are considered). It is proved 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 some of them are generalized using certain new methods). Mostly, the version of $w_{\mathrm {Chow}}$ 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.

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Additional Information

**M. V. Bondarko**

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

Email:
mbondarko@gmail.com

**M. A. Ivanov**

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

Email:
micliva@gmail.com

Keywords:
Voevodsky motives,
triangulated categories,
weight structures,
Deligne’s weights,
$cdh$-topology

Received by editor(s):
April 12, 2015

Published electronically:
September 30, 2016

Additional Notes:
Supported by RFBR (grants no. 14-01-00393A and 15-01-03034A). The first author is also grateful to Dmitry Zimin’s Foundation “Dynasty”

Dedicated:
Dedicated to S. V. Vostokov, our Teacher in mathematics and in life

Article copyright:
© Copyright 2016
American Mathematical Society