Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

Request Permissions   Purchase Content 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 14C15, 19E15, 14C25, 14F20, 14E18, 18E30, 13D15, 18E40

Retrieve articles in all journals with MSC (2010): 14C15, 19E15, 14C25, 14F20, 14E18, 18E30, 13D15, 18E40


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

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