Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

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



On Chow weight structures without projectivity and resolution of singularities

Authors: M. V. Bondarko and D. Z. Kumallagov
Translated by: M. V. Bondarko
Original publication: Algebra i Analiz, tom 30 (2018), nomer 5.
Journal: St. Petersburg Math. J. 30 (2019), 803-819
MSC (2010): Primary 14C15
Published electronically: July 26, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper certain Chow weight structures on the ``big'' triangulated motivic categories $ \mathrm {DM}^{\mathrm {eff}}_{R}{}\subset \mathrm {DM}_{R}$ are defined in terms of motives of all smooth varieties over the ground field. This definition allows the study of basic properties of these weight structures without applying resolution of singularities; thus, it is possible to lift the assumption that the coefficient ring $ R$ contains $ 1/p$ in the case where the characteristic $ p$ of the ground field is positive. Moreover, in the case where $ R$ does satisfy the last assumption, our weight structures are ``compatible'' with the weight structures that were defined in previous papers in terms of Chow motives; it follows that a motivic complex has nonnegative weights if and only if its positive Nisnevich hypercohomology vanishes. The results of this article yield certain Chow-weight filtration (also) on $ p$-adic cohomology of motives and smooth varieties.

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

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 14C15

Retrieve articles in all journals with MSC (2010): 14C15

Additional Information

M. V. Bondarko
Affiliation: St. Petersburg State University, Universitetskii pr. 28, 198504 St. Petersburg, Russia

D. Z. Kumallagov
Affiliation: St. Petersburg State University, Universitetskii pr. 28, 198504 St. Petersburg, Russia

Keywords: Triangulated categories, weight structures, Voevodsky and Chow motives, Deligne weights, compact objects, t-structures.
Received by editor(s): March 24, 2018
Published electronically: July 26, 2019
Additional Notes: The work of the first author on Sections 1, 2.2, and 3.1 of this paper was supported by the Russian Science Foundation grant no. 16-11-10200.
Article copyright: © Copyright 2019 American Mathematical Society