Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

Intersecting the dimension and slice filtrations for motives

Pages: 259 – 274

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n1.a16


Mikhail V. Bondarko (Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia)


In this note we prove that the intersections of the levels of the dimension filtration on Voevodsky’s motivic complexes over a field with the levels of the slice filtration are “as small as possible”. This statement is applied to prove that a conjecture of Ayoub is equivalent to a certain orthogonality assumption.


Voevodsky motive, dimension filtration, slice filtration, weight structure, triangulated category, Chow motive

2010 Mathematics Subject Classification

Primary 14C15, 18E30. Secondary 14C25, 18E35, 19E15.

Research is supported by the Russian Science Foundation grant No. 16-11-10200.

Received 16 June 2017

Received revised 13 November 2017

Published 21 February 2018