2016/03/30 by Bondarko, Mikhail V.
#14C15 #14C25 #14F20 (Secondary) #18E30 (Primary) #18E35 #18G40 #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.1603.09330
In this paper we prove that the intersections of the levels of the dimension filtration on Voevodsky's motivic complexes over a field k with the levels of the slice one are "as small as possible", i.e., that Obj d≤ mDMeff-,R ∩ Obj DMeff-,R (i)=Obj d≤ m-i DMeff-,R (i) (for m,i≥ 0 and R being any coefficient ring in which the exponential characteristic of k invertible). This statement is applied to prove that a conjecture of J. Ayoub is equivalent to a certain orthogonality assumption. We also establish a vast generalization of our intersection result to relative motivic categories (that are required to fulfil a certain list of "axioms"). In the process we prove several new properties of relative motives and of the so-called Chow weight structures for them.