On Chow weight structures for $cdh$-motives with integral coefficients
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- by M. V. Bondarko and M. A. Ivanov
- St. Petersburg Math. J. 27 (2016), 869-888
- DOI: https://doi.org/10.1090/spmj/1424
- Published electronically: September 30, 2016
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Abstract:
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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Bibliographic 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
- 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”
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3589220
Dedicated: Dedicated to S. V. Vostokov, our Teacher in mathematics and in life